Nghiên cứu ứng dụng các phương pháp hiện đại nhận dạng sự cố ngắn mạch trên đường dây truyền tải điện tt tiếng anh

-1-

INTRODUCTION
1. The thesis justification
The power electric system is a complex system in both structure and operation so the faults of any
element in the system will affect the power supply reliability and power quality. Therefore the main topic of
this thesis is “Research and apply modern methods to detect the fault on the transmission line”. The
proposed methods will help to quickly identify and locate the faults on transmission lines to reduce the
economic losses and to improve the reliability and quality of electricity supply to the consumers is very
necessary.
The problem of detecting the type of fault and the location of the fault on the power transmission line is a
basic problem of circuit theory and power system. Currently, many researchers has been working on this
issue. However, the results are still limited due to the fact that many fault events and faulty element values
cause phenomena similar to the variations of parameters of the line, so methods such as distance relays will
cause big errors. The development of new measuring devices as well as new signal processing algorithms
can further improve the accuracy of the fault location estimation.
A new solution to analyze and detect fault locations will have practical implications. If results can be
applied, it will bring about high economic and technical efficiency due to the increased accuracy to support
the faster fault process.
Research purposes: The purpose of the thesis research is to develop a new method using modern
algorithms to allow the faults location on the power transmission lines (without branching and with
branches) more accurately with as few measuring devices as possible.
Research scope: The thesis focuses on researching and providing methods to locate the faults on nonbranched and branched transmission lines. The thesis hasn’t considered the influence of environmental
factors such as temperature and humidity on accuracy of the method.
Research focuses of the thesis: Research on signal analysis and processing algorithms using Matlab
tools, wavelets, neural networks, correlation functions, Time-Domain Reflectometry (TDR) and TimeDomain frequency Reflectometry (TDFR) to identify fault locations and types of fault on transmission lines
that single branch and transmission lines have many branches. Study the effect of fault resistance, fault
inductance to the accuracy of the method.
Research Methods: Analyze the system and identify the characteristics of the study object through many
different approaches. Select and build the mathematical tools needed for research. Select evaluation tools and
verify the research results, as simulation modeling with Matlab software and test fault identification

algorithms.
Scientific and practical significance of the thesis:
The main scientific meaning of the thesis is: proposing a new method of identifying the fault location on
the transmission line to supplement the existing methods, built and solved the problem of accurate fault
location with different types of faults.
Practical significance of the thesis
The research results of the thesis can be added to solutions to locate fault on transmission lines with one
or more branches. The method only requires at least the measurement signals from the ends of the power
transmission line, so the measurement and data collection stages are simple and highly economical.


2

CHAPTER 1
OVERVIEW OF FAULT IDENTIFICATION AND LOCATION ON
TRANSMISSION LINE
1.1 Introduction
1.2 Overview of methods to detect faults on the transmission lines.
1.3 Method of measurement from one side
1.3.1. Single reactance method
1.3.2. The Takagi method
1.3.3. Improved Takagi method
1.4. Method of measurement from two ends
1.5. The method uses neural network
1.6. Method of wave propagation
1.6.1. The method of locating incidents is based on the principle of propagation from the fault.
1.6.2. Method of wave propagation from line ends
1.7. Conclusion:
When reviewing the methods of fault location on the tranmission line, it can be summarized that there
are classic methods such as the measurement method from one end of the line and the measurement methods

from two ends of the line. As new methods we can list the neural networks and wave propagation methods.
Each of methods and algorithms is different, as its advantages and disadvantages.
The types of the transmission lines are very diverse: there are transmission lines with different voltage
levels, one source or multiple supplies, single lines, double lines, lines with one or many branches.
The nature of the fault is also different as the resistance and inductance of the fault change. Therefore
one method can’t be applied to all types of transmission lines. Simple solutions such as the single reactance
method are as easy to implement but the accuracy isn’t high.
The measurement method from two ends of the line or the method based on the wave from the fault
point is more accurate but it uses many devices and requires synchronous time, leading to complicated and
costly.
The thesis focuses on researching solutions for three-phase (single branch and multiple branches)
three-phase power transmission systems with the requirement to use as few measuring devices as possible
and do not require time synchronization.
In the following chapters, the thesis will focus on the method of proactively generating pulses from the
beginning of transmission lines to identify faults. Because the method uses few devices, no synchronization
is required. This thesis researchs time domain reflectometry (TDR) and time frequency domain reflectometry
(TFDR) method basing on the analysis of reflected waveform to detect fault on the transmission lines.


3

CHAPTER 2
SOLUTIONS ON THE BASIC ANALYSIS OF THE WAVE
PROPAGATION COMPONENTS
2.1. Mathematical models of wave propagation on transmission lines
2.1.1. Transmission line model
In order to simulate transmission lines according to [2], [22] often use model  and model of distributed
line parameters (Distributed Parameter Line).
a) Model :

An approximate model of the distributed parameter
line is obtained by cascading several identical 
sections, as shown in the following figure.

Fig 2. 1: Single-phase  transmission line model
Fig 2. 2: Three-phase  transmission line segment model

b) Model parameters transmission lines
According to [2], [22] state equation of long
line is:
i (x, t)
 u (x, t)
  x  R  i (x, t)  L  dt

 i (x, t)  G  u (x, t)  C  u (x, t)

dt
t
Fig 2. 3: Diagram of Distributed Parameter Line

where R, L, C, G is parameters of lines per unit length.
2.1.2. Principle of wave propagation on the transmission lines
According to [6], [22] wave propagation on the line includes forward u+(x,t) and reflective wave u-(x,t),
Parameters typical for long-distance transmission are included: the surge impedance ZC, coefficient off ,
phase factor , Speed of wave v.

Z0
R0  j L0

 Z0e j

Y0
G0  j Go

a) Characteristic impedance is:

ZC 

b) Propagation constant is :

    j  ZY

c) Propagation speed:

v

 2

 f    f where  is wavelength, f is the frequency.
 

According to [3] when the line has characteristic impedance of the line Z0 and load impedance Z2. The 
(reflection coefficient) and  (refraction coefficient) can be expressed by the following formula:
2Z 2

and   V ref  Z 2  Z 0 


Z0  Z 2
V inc
Z2  Z0

where, Vref is amplitude of the reflected signal, Vinc is amplitude of the forward signal.


4

2.1.3. Wave propagation on a faul-free transmission line
When t = 0, we switch on a voltage source Vinc (t ) to the beginning of the line. According to [6] when the
line has characteristic impedance of the line Z0 and load impedance Z2.
The  (reflection coefficient) and 
(refraction coefficient) can be expressed
by the following formula:



V
2Z 2
Z  Z0
và   ref  2
Z0  Z 2
Vinc Z 2  Z 0

Fig 2.4: Equivalent Petersen model for solving the wave propagation

where, Vref is amplitude of the reflected signal, Vinc is amplitude of the forward signal.
When the line has no fault, the time of wave spreads from beginning to end of line is calculated as in the
following formula:


 t  t 2  tl 

2 l

v



where, t1 is point time of voltage switching and t2 is the return time point of reflected signal from the end of
the line.
a) Wave propagation on a faul-free transmission line with resistance load
According to [6], when switching on a
voltage source Vinc (t ) at the beginning of the
line, if the line has characteristic impedance of
the line Z0 and load impedance Rt, the 
(reflection coefficient) can be expressed by the

Fig 2.5: Equivalent Petersen model for lines with resistive load

following formula:

Vref    Vinc 

Rt  Z 0
Vinc
Rt  Z 0

b) Wave propagation on the transmission line does not have fault with resistance serial
inductance load :
On Fig.2.6, the circuit solution has the voltage
signal measured at the beginning of the line after 1st
reflections as:

t
 R
 
Z0
t
T
Vtd (t )  2  Vinc 

e 
 Rt  Z 0 R  Z 0


Fig 2.6: Equivalent Petersen model for lines with R-L
serie load

c) Wave propagation on a faul-free transmission line with R-L parallel load
The circuit on Fig. 2.7 has:
t
 R
 
T
Vtd (t )  2  Vinc 
*e 
 R  Z1


where: T 

R  Z1
L

R  Z1

Fig 2.7: Equivalent Petersen model for lines with R-L


5
parallel load

d) Wave propagation on the transmission line does not have fault with resistance parallel
capacitive load :
The circuit on Fig. 2.8 has:
t 
 R

t
Vtd (t )  2  Vinc 
 (1  e T ) 
 Rt  Z 0


where: T 

Rt  Z0
 Ct time coefficient. When t=0 has
Rt  Z 0

Fig 2.8: Equivalent Petersen model for lines with RC parallel load

Vtd (0)  0

e) Wave propagation on a faul-free transmission line with R-C serie load
On Fig.2.9, the circuit solution has the
voltage signal measured at the beginning of
the line after 1st reflections as:
t

 
2.Rt
T
Vtd (t )  Vinc   2 
e 
Rt  Z 0



Fig 2.9: Equivalent Petersen model for lines with R-C serie load

where T  ( R  Z 0 )  C.
2.1.4. Wave propagation on a faulty transmission line:
When the forward wave spreads from the beginning of transmission line to the fault location, it will cause
a reflective wave back to the beginning of the transmission line. we consider the case of temporary the short
circuit with fault resistance and fault inductance Z fault  R f  j  X f .
The reflection coefficient at the fault location is: 1 

Z 0  Z 0
Z 0  Z 0

If the line is not open (due to the work of the protection devices), the wave refraction will continue to
come to the end of the transmission line and again reflect back from there. where Z 0  Z fault || Z 02 . The
reflector components back to beginning line can be expressed by the following formula:

Vref 1  1Vinc 

Z0
 Vinc
2  Z fault  Z 0

And refractive components spread to the end of transmission line as: 1  1  1 .
Vinc 2  (1  1 )  Vinc

Refractive components spread to the end of the transmission line when it met the loads at the end of the
line. At that time, we will have a reflected waves. The reflection coefficient can be expressed by the
following formula:

2 

Zt  Z0
Zt  Z 0

2.2. The proposed solutions in the thesis
2.2.1. Diagram of the block estimating the fault location
The thesis proposes two methods of reflected wave analysis TDR and TFDR.


6

Pulse

Tranmis
sion
line

Signal feedback
From free fault line
Signal feedback
from fault line

Block
collected,
storage

Detect feedback
time when the line
is free faulty

Calculation of
propagation
speed

Detect the time of feedback
from the fault point

Estimated
results
fault
location

Fig 2.10: Block diagram of method overview to identify fault locations on power transmission lines.
2.2.2. Time domain reflectometry method basing on the analysis of reflected waveform for lines without
branches:
The thesis proposes to use TDR method for transmission lines without branching. This method will use a

pulse generator circuit (voltage /current) at the beginning of the transmission line. After sending the pulse
into the line, we will track and record the reflected signal. The analysis of reflected waveforms on the
transmission lines to detect the fault location.
This thesis proposed using wavelet to
determine the time point of reflected signal from
the transmission line which causes a sudden
variable voltage signal at the beginning of
transmission line.
The signal after wavelet analysis preliminarily
determines the time point of reflected signal will
be put into the neural network or use analytical
algorithm to estimate the fault location, as on Fig.

Fig 2. 11: Block diagram to identify fault locations on the
transmission lines

2. 11.

With the tranmission line has no branch but requires high accuracy (or the line may have many lines in
a serialized system), the thesis proposes to use TFDR method. The main content of this method use a circuit
to generate a chirp signal (signal with amplitude and frequency changes over time) at the beginning of the
line, then analyze the feedback signal to locate the fault.
2.2.3. Methods of analyzing feedback waves with multi-branch lines.
2.3 Simulation method to test research results based on Matlab / Simulink tool
2.3.1 Simulating wave process on the transmission lines:
The thesis uses Matlab/Simulilnk software to
simulate the wave transmission process on the
transmission line in case the line has no branch
and the line has many branches with different
types of fault parameters. The idea for this

model is shown in Figure 2. 12.
Fig 2. 12: Model of simulating wave propagationon the
transmission lines

2.3.2 Building elements used in the simulation


7

Fig 2. 13: Block diagrams simulating fault forms, DC

Fig 2. 14: A block model measures the feedback signal

sources, chirp signal sources

from the fault point and the end of the line.

2.4. Conclusion
Based on the analysis of advantages and disadvantages of previous studies, the thesis has proposed
solutions to identify fault on 3-phase transmission lines:
 Using the TDR application method to detect locations of fault based on analysis time and wave shape
of the reflected signal on the transmission line using Wavelet and neural network analysis,
 Using the TFDR application method to detect locations of fault based on analysis time and wave
shape of the reflected signal on the transmission line using correlation function analysis,
 Proposing the application of Matlab / Simunlink software as a simulation tool to test the research
results.

Chapter 3:
TDR METHOD TO DETERMINE FAULT ON THE TRANMISSION LINE
3.1. Method description

When faults occurred, the protection element
reacted to isolate the faults. Later we need to locate
the position of the fault. One of the proposed
methods is the time domain reflectometry (TDR).
This method will use a pulse generator circuit
(voltage

/current)

at

the

beginning

of

the

Fig 3. 1: The working principle of Time Domain
Reflectometer

transmission line.
After sending the pulse into the line, we will track and record the reflected signal. The analysis of
reflected waveforms on the transmission lines allow to detect the fault location and to estimate the fault
resistance and the load characteristics.
3.2 Application of wavelet decomposition in detecting the sudden change time of sign:
3.2.1 Spectrum analysis by wavelets:
3.2.2 Wavelet transform algorithm discrete:
Continuous Wavelet Transform - CWT of a function f(t) is started from a function wavelet (Mother

Wavelet) ψ(t).
3.2.3 Wavelet algorithm analyzes the reflected signal:


8

Wavelet is a very effective tool to detect the time point of sudden signal changes. When using wavelet, a
time-dependent signal can be analyzed as follows: f (t)  a(t)  d(t) . Where: a(t) is component
“approximation” that contains slowly variable components and d(t) is component “detail” that contains fast
variable components. We can continue the same analysis for the component to get multistage wavelet
spectrum analyzer as follows:
f ( t )  a1 ( t )  d1 ( t )
a1 ( t )  a 2 ( t )  d 2 ( t )
...
a k ( t )  a k 1 ( t )  d k 1 ( t )

For example, we use wavelets to analyze the
signal of the function as follows:
0  t  500
 sin(0.1t )
y (t)  
sin(0.101t ) 500  t  1000

Figure 3.3 shows the graph of the function y(t),
Fig.

3.4

shows

detail

component

d1

and

approximation a1 component of the signal from Fig.
3.3. From the results of the analysis, the signal y(t) is
analyzed to the detailed component

d1 and

approximation. When we calculate the detailed
component level 1 (component d1 of the signal) as
shown in Fig. 3.4. We can see all the sudden

Fig 3.2: The structure of successive steps analyzes an

variation of the signal in Figure 3.4 will correspond

initial signal into detailed and approximate components

to the sudden huge increase of component d1. So
wavelet is a very effective tool to determine the time
of this fault.
Approximation A1

1

1

0.8
0.5

0.6
0.4

0

0.2

-0.5

0

-1
0

-0.2
-0.4

200

300

400

500

Detail D1

600

700

800

900

1000

100

200

300

400

500

600

700

800

900

1000

0.1

-0.6

0

-0.8

-0.1

-1

100

0.2

0

100

200

300

400

500

600

700

800

900

1000

Fig 3.3: Signal of function y(t)

-0.2
0

Fig 3.4: Daubechies wavelet spectrum analysis of y(t)
signal

In this thesis, they proposed using wavelet 4-th order Daubechies type to determine the time point of
reflected signal from the transmission line which causes a sudden variable voltage signal at the beginning of
transmission line. Figure 3.5 shows the form of the reflected voltage signal at the beginning of the lines when
there is a 3-phase fault at 20km (the load is a Rload in series with a Lload). Figures 3.5, 3.6 shows signal the
measured signal which has two sudden times very clearly at t =~ 2 ms. It was the time that the voltage source
turned on to the line. At t  2,17 ms is the reflected voltage from the fault arrives back, t  2, 4ms is the
reflected signal from the end of the line arrives.


9

When we calculate the detailed component level 1 (component d1 of the signal) as shown on Fig. 3.5 and

(and zoomed in on Fig.3.6), we can see the sudden variation of the signal in Fig. 3.5 will correspond to the
sudden huge increase of component d1. So wavelet is a very effective tool to determine the time of this fault.
Detail D1

70

40

60

30

50

20
10

40

0

30
-10

20
-20

10
0
0

-30

0.5

1

1.5

2

2.5

3

3.5

4.5 -400

4

Time(s)

x 10

0.5

1

1.5

2

-3

2.5

3

3.5

Times(s)

4

4.5
x 10

4

Fig 3.6: Form of the reflected voltage signal at the beginning of the lines when there is a 3-phase resistive fault at 20km
(the load is a Rload in series with a Lload) and detail component d1 of the voltage
Detail D1
5
4
3
2
1
0
-1

-2
-3
-4
-5
0

0.5

1

1.5

2

2.5

3

3.5

4

Times(s)

4.5
x 10

4

Fig 3.7: Detail component d1 of the voltage signal from Fig. 3.5 is zoomed in

Steps calculate to determine specific time of voltage signal at beginning of transmission line as follows:
Step 1: At time t0, using a pulse generator circuit

Step 7: The time point T0 corresponds to the time

(voltage/current) at the beginning of the transmission

point that the waves reflected from the end of the

line after the fault has occurred and the protective line ( when no fault accured). With the length of the
0  t  T0
V
elements have reacted u (t)   inc
. The line is 46.7km, time of propagation and reflected
t  T0
waves in line will be approximately 0,4ms. So T0
 0

d1 (t )   .
time point T0 corresponds to the time point that the approximately 2,4ms. Choose T0  t min
2,4 ms
input wave propagated to the end of the line and
reflected back to the beginning of the line.
Step 2: Measure the reflected signals at the
beginning of the line with sampling frequency  and

Step 8: If there is a time that value of d1 greater than
the threshold (difference with the reflected signal
from load), then it shows that a fault ocurred in the a

point along of the line. t1  min d1 (t )   .
t0 t T0

measurement time t> T0.
Step 3: Perform wavelet transform to get W(a, b)
from u (t0, T0);

Step 9: If this location doesn’t exist, let    / 2 . If

  0.025 then go back to step 7.

Step 4: Calculate component d1 of 4-th order

Step 10: If there is no point, where value d1 exceeds

Daubechies wavelet expansion.

the threshold on the line, then the line hasn’t fault.

Step 5: Determine the time at which d1 values are
greater than the threshold 0.1.
Bước 6: The first time t 0 corresponds to the time of
closing the pulse generator (in this thesis, it is chosen
at 2ms): t0  min d1 (t )   . where   0,1;
t  2 ms

The location of the fault point (if it exists) will be
t t
t
calculated by formula: x  v   v  1 0 where:

2
2
v  wave speed on the transmission line, mean as:
v

2l
where T0  t0
T0  t 0

is the time the wave

propagated and reflected from the end of the line.


10

3.2.4 Factors contributing to the accuracy of wavelet analysis in detection of the reflectd waves:
3.3 Fuzzy neural network and application to correct the time of wave response
3. 3.1 TSK fuzzy logic rules
TSK (Takagi – Sugeno - Kang) fuzzy neural network model is built with learning algorithm to adjust the
network parameters to fit a given sample data sets [10]. This network is characteristic in parallel processing
of a set of inference rules. The TSK model uses fuzzy logic rules as:
N

If x A then y  f (x)  q0   qi xi where: qij are linear constants, x is the input vector x   x1, x2 ,, xN  .
i 1

3.3.2 TSK fuzzy neural network
model

x
W 1(x1=A11

The TSK model was implemente

x1
W 2(x2=A1

.
.

as a straight-forward network as on
Fig.

3.7.

The

network

x

is

characterized with 3 parameters (N,

x2

W 1(x1=A2

Y2=f2(

F1

W(xA2

W 2(x2=A2

.
.

M, K) where N is the number of

Y=f(x)

W N(xN=A2

inputs (the components of input

x

vector x), M is the rules number, K
is the outputs number. In general,

Y1=f 1(

W(xA1

X

W(xA

W 1(x1=AM

YM=f M(x)

W 2(x2=AM

.
.

TSK can be considered as a 5-layer

F2

W N(xN=AM

network.

Fig3.8: TSK fuzzy neural network

3.3.3 Mathematical formulas of TSK fuzzy neural network
[10] proposed an adaptive adjustment algorithm into two processes of adjusting linear parameters and
adjusting nonlinear parameters. The algorithm is described as follows:


Step 1: Initialize the initial values of nonlinear and linear parameters.



Step 2: Maintain the value of linear parameters, using the maximum step reduction algorithm to
adjust the nonlinear parameters.



Step 3: Maintain the values of non-linear parameters, using algorithm to adjust linear parameters.



Step 4: Check the objective error function, if E learning process, otherwise return to step 2.

3.3.4 Initiating neural networks for learning process
3.3.5 Fuzzy clustering algorithm
3.3.6 TSK network to correct the time of the feedback wave
Let denote the reflected signals y j   y1 j , y 2 j ,  , y Nj  . Using the wavelet decomposition to find the
sudden changes in the signal (marked as t1 ) as shown above, in this thesis 20 values were sampled around t1
with

sampling

step

1ms

t1  h(ms)

y   y (t1  h), y (t1 ),........... y (t1  18  h) .

for

h  1,0,1,...,18. ,

corresponding

to

20

values


11

70

70

60

65
60

50

55
40

50

30

45

20

40

10

35

0

30
25

-10

20
-20

0

0.5

1

1.5

2

2.5

3

3.5

4

Time (ms)

4.5

2.085

2.09

2.095

2.1

4

x 10

2.105
Time (ms)

2.11

2.115

2.12

2.125
4

x 10

Fig 3.9: Form of the reflected voltage signal at the

Fig 3.10: Zoomed in signal from Fig.3. 8 at the 1st

beginning of the lines when there is a 3-phase fault at

reflection

10km (the load is a R series with a L).

Figure 3.8 shows the form of the reflected voltage signal at the beginning of the lines when there is a 3phase fault at 10km. Figure 3.9 shows the zoomed in signal from Fig.3. 8 at the 1st reflection. The thesis
using wavelet analysis to determine relatively accurate the time of arrival of the reflected signal on
transmission lines to take sample extract data as shown in Fig. 3.10.
The thesis has proposed the TSK fuzzy logic

75

neural network with 20 inputs (corresponding to 20

65

values
in
the
extracted
y   y (t1  h), y (t1 ),........... y (t1  18  h)  )

55

signal
and one

70

60

y(to)

50
45
40

output s. Where s is the error between the time of

35

arrival of the reflected signal from the point of fault

25

at the beginning of the transmission line and the
time t1 estimated by wavelets.

30
0

2

4

6

8

10

12

14

16

18

20

Time (micro second)

Fig 3.10 Example of sampling 20 probes starting from the
beginning of the signal

3.4 Simulation results and calculations when using TDR method
3.4.1 Simulation model of propagating waves using Matlab Simulink
This thesis uses Matlab – Simulink to build models which simulate the wave propagation on the lines.
The parameters of 171-110kV Lào Cai the simulation line are: l AB  46, 7 km ; the length of the line;
L0  25, 7  H km ; the inductance per unit;
R 0  17, 43 m  / km ; the resistance per unit length, and
C 0  6, 991  F km ; the capacitance per unit length.

Simulation model as shown in
Figure 3.11 with a pulse generator
and fault-free transmission line.
Figures 3.12 and 3.13 show the
simulation

model

to

find

the

incoming wave and the reflected
wave

of

a

faulty

3-phase

transmission and a faul-free load –
free 3-phase transmission line.

Fig 3.11: Simulation model to find the incoming wave and the reflected
wave of a faul-free 3-phase transmission line with


12

Fig 3.12 Simulation model to find the incoming wave and

Fig 3.13 Simulation model to find the incoming wave and

the reflected wave of a faulty 3-phase transmission

the reflected wave of a faul-free load –free 3-phase
transmission line

3.4.2. Results of simulation wave propagation from Matlab-Simulink
a) The line without fault
Using the model in Figure 3.11 to simulate the load in cases R, R series L, R parallel C and combine with
running the program in Matlab as Appendix 1. We get the results as shown in Figs. 3.14, 3.15 and 3.16.
70

70

60

60

50

50

40

40

30

30

20

20

10

10

0
0

0.5

1

1.5

2

2.5
Times

3

3.5

4

0
0

4.5

0.5

1

1.5

2

2.5
Times

3

3.5

4

4.5

5
x 10

-3

Fig 3.14: The form of the voltage at the beginning of

Fig 3.15: The form of the voltage at the beginning of the

the line when the load is purely resistance

line when the load is parallel R-C ( Rloadi =100(), C=1µF).

Rload=100().
120
110

100

100
90

80

80

60
70

40

60
50

20

40

0

0

0.5

1

1.5

2

2.5
Times

3

3.5

4

4.5

2.35

5
x 10

2.4

2.45

2.5

Times

-3

Fig 3.12: The form of the voltage at the beginning of

Fig 3.13: Zoomed in signal from Fig.3.16 at the 1st

the line when the load is series R-L(Rload=100(),

reflection

x 10

-3

L=10mH)

When the line has no fault, Daubechies wavelet level 4 analysis reflected waveform and combined with
the algorithm was used to find t2 (the time point that the reflected signal returned from the end of the line).
With the t0 (the point time of the sending wave) is known, the speed of the wave on power transmission lines
is calculated by formula (3.20). The calculation results are shown in Table 3.1.
TABLE 3.1: Speed

of wave on the transmission line

t0 (s)

t2 (s)

v (km/s)

2

2.4043

231.106,5

b) Tranmission line with fault:
Single-phase to ground account for 60% of faults in electrical systems. A 1-phase fault with fault

resistance Rfault = 10 (Ω) and Lfault = 0,5mH has the results shown in Figure 3.18a and Figure 3.18b.


13

b)

a)
70

70

60

60

50

50
40

40

30

30

20
20

10
10

0
0
0

0.5

1

1.5

2

2.5
Times

3

3.5

4

4.5

5
x 10

-10

-3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5
x 10

-3

Fig 3.14 : Form of the reflected voltage signal at the beginning of the lines when there is a 1-phase fault at 20km a)
Rfault=10 , Rload=100. b) cố Rfault=10 and Lfault=0,5mH, Rload=100.

3-phase fault (ABCG) with fault resistors Rfault = 10(Ω), Lfault = 0.1mH with different load types have the
results as shown on Figs 3.19, 3.20, 3.21, 3.22 and 3.23.
70
60
50
40
30
20
10
0
0

0.5

1

1.5
Times

2

2.5

3
x 10

-3

Fig 3.15: The form of voltage wave at the beginning of the 3-phase line when there was a 3-phase shortage fault at

l=20km (with the load was Rload=100 in parallel with Cload=1µF).
70

70

60

60

50

50

40

40

30

30

20

20

10
0

10
1.5

2

2.5

Times

3
x 10

0

1.5

-3

2

2.5

Times

3
x 10

-3

Fig 3.16: Form of the reflected voltage signal at the

Fig 3.17: Form of the reflected voltage signal at the

beginning of the lines when there is a 3-phase resistive

beginning of the lines when there is a 3-phase resistive fault

fault at 20km (the load resistance is Rload=10,

at 20km (Rfault=10, load R series L, Rload=100, Lload=1

Rfault=10 )

mH)

70
60

65

50

60
55

40

50

30

45

20

40
10
35
0
0

0.5

1

1.5

2

2.5
Times

3

3.5

4

4.5

5
x 10

2.145

-3

2.15

2.155

2.16

2.165

2.17
Times

2.175

2.18

2.185

2.19

2.195
x 10

Fig 3.18: Form of the reflected voltage signal at the

Fig 3.19: Zoomed in signal from Fig.3.22 at the 1st

beginning of the lines when there is a 3-phase resistive

reflection

-3

fault at 20km (the load resistance is Rload=10,
Rfault=10 series Lfault=0,1mH)

2-phase fault (AB) and 2-phase fault ground (ABG) at 20 km with fault resistance R fault= 0 (Ω) and resistive
load have the results as shown in Figure 3.24 and Figure 3.25.


14
70

70

60

60
50

50

40

40

30

30
20

20
10

10
0
0

0
0

0.5

1

1.5

2

2.5
Times

3

3.5

4

4.5

0.5

1

1.5

5
x 10

2

2.5
Times

3

3.5

4

4.5

5
x 10

-3

-3

Fig 3.20: The form of voltage wave at the beginning
of the 3-phase line when there was a 2-phase

Fig 3.21: The form of voltage wave at the beginning
of the 3-phase line when there was a 2-phase-earth
shortage fault at l=20km (Rfault=10, load

shortage fault at l=20km (Rfault=10 , load

Rload=100)

Rload=100)

3.4.3 Use wavelet analysis to estimate results
Using 4-th order Daubechies wavelet to analyze the reflected waveforms on the transmission lines to
detect the fault location.
Table 3. 2: Calcutation of distance to fault point with
three ground phase fault.

LFault
(km)
10
20
30
40
50

Table 3. 3: Calcutation of distance to fault point with
three ground phase fault at lfault=20 km

Rfault
()

LFault
(mH)

10

0

Calculated
distance l
(km)
10.066

Error
[m]

Rfault
()

LFault
(mH)

L (km)

Error

[m]

66

5

0

20.070

70

10

1

10.402

400

10

0

20.070

70

10
10

10
10
10
10
10
10

0
1
0
1
0
1
0
1

20.070
20.370
30.021
30.357
40.061
40.379
50.047
50.401

70
370
21
357
61

379
47
401

15

0

20.070

70

20

0

20.070

70

10

1

20.370

370

10

5

20.317

317

10

10

20.543

543

Table 3. 4: Calcutation of distance to fault point with 1 ground phase fault and 2 ground phase fault at lfault=20 km

Fault type
AG

ABG

AB

lFault (km)
20
20
30
30
20
20

30
30
20
20
30
30

Rfault ()
10
10
10
10
10
10
10
10
10
10
10
10

LFault(mH)
0
1
0
1
0
1
0
1

0
1
0
1

L (km)
20.070
20.232
30.021
30.289
20.070
20.245
30.021
30.285
20.079
20.234
30.030
30.305

Error [m]
70
232
21
289
70
245
21
285
79
234

30
305

From models such as Figure 3.12 and Figure 3.13, testing 400 cases with different types of fault resistors
and with different types of fault gives the results as in Appendix 02. From these results, the average error of
the estimated location of the fault is:


15

Eaverage 

1 400
 li _ estimated  li_dest  0,0523(km)  52,3(m)
400 i 1



Corresponding to relative error: E%_average 



1 400 li _ estimated  li_dest
 0,26(%)

400 i 1
li_dest

From models such as Figs 3.12 and 3.13, testing 800 cases with different types of fault inductance and
with different types of incidents gives the results as in Appendix 3. From these results, the average error of

the estimation of the fault location is:

Eaverage 

1 800
 li _ estimated  li_dest  0,550(km)  550(m)
800 i 1



Corresponding to relative error: E%_average 



1 800 li _ estimated  li_dest
 2,75(%)

800 i 1
li_dest

4.2.3 Results of correcting the fault location with TSK neural network
This thesis use the transmission lines model described in Fig. 3.12 when changing some input parameters
to generate the data sets as:
 Fault location: N = 8 positions (5, 10, 15, 20, 25, 30, 35, 40km).
 Fault resistance Rsc: K = 3 values (1, 5, 10 Ω).
 Fault types: P = 4 types (1 phase fault, 2 phase fault, 2 phase grounded fualt, 3 phase fault).
 Fault inductance: Q = 5 cases (0; 0,1; 1; 1.5 ; 2 mH)
The total number of simulations with to the fault location,

fault resistor, fault type:

N  K  P  Q  8  3 4 5  480 cases.
With simulated data, the thesis has written a program including:


Appendix 6: Writing density function pre_substr.m to use for initializing Subtractive Clustering
algorithm.



Appendix 7: SubtractiveClustering algorithm program.



Appendix 8: Program: tsk_learn.m Using maximum step reduction algorithm to adjust nonlinear
parameters and method of analyzing singular coefficients to adjust linear parameters



Appendix 9: Program: tsk_test.m to check trained TSK network

With a sample dataset of M = 480 simulated samples, in this paper, the thesis will randomly take 360
samples to learn and 120 random to check the quality of the network built from the original dataset.
With the given data set, the TSK network had 20 inputs (corresponding to 20 values in the extracted
signal y   y (t  h), y (t  2h),........... y (t  18  h)  ) and one output is the arrival time error generated. Conduct
training neural network with adaptive coefficient system as described in 3.5.7 with arithmetic coefficients
  0.001 . When the steps are good E (k)  E (k 1)     *1.05 , the learning coefficients
increase  inc  1.05 . When the learning step is too large E (k)  E (k 1)     *0.7 , the learning step
reduction factor  dec  0.7 .
Errors allowed in learning process is equal to 0.01 means E (k)  1.01* E (k 1) . Conduct training for 200

learning steps in which: 10 - step adjusting nonlinear parameters / 1 step adjusting linear parameters. The


16

results of the learning process are shown in Figure 3.26 and Figure 3.27. Where Figure 3.26 is the shape of
the output response of the TSK network. Figure 3.27 shows the error between output response and learning
outcome.
600

90
Destination
TSK Output

80

500
70
60
Error (micro second)

400
50
40
30

300

200

20
10

100
0
-10

0

50

100

150

200
Learning sample

250

300

350

0

400

Fig 3.22: The output from the TSK network and the

0

50

100

150

200
Learning sample

250

300

350

400

Fig 3.23: Graph of errors between learning results and

expected values

input data

90

500
Destination
TSK Output

80

450

400

70

350
Error (micro second)

60

50

40

30

300

250

200

150

20

100

50

10

0
0

0

20

40

60
Testing sample

80

100

0

20

40

60
Testing sample

120

Fig 3.24: Graph of test output response of TSK network

80

100

120

Fig 3.25: Graph of errors between test results and input
data
n

( yk  dk )2
The average error of n data sets is calculated by the formula:

Et 

k 1

n

.

The average error of the 360 sets of data is calculated as: 0,3791µs, with the largest error of the result of
5,022µs.
3.5. Testing design and manufacturing TDR equipment using FPGA
3. 6 Conclusion Chapter 3

In this thesis, the author has presented the following contents:
 Presenting TDR application method to detect locations of fault and load parameters based on analysis
time and wave shape of the reflected signal on the transmission. Based on the time of pulse generation
and the time of wave response from the point of fault to locate the problem.
 Presentation of the method of application of fuzzy logic neural networks to improve fault location
errors based on feedback waves.

Chapter 4: TFDR METHOD TO DETERMINE FAULTS ON THE BRANCHED
TRANSMISSION LINES
4.1 Description of the TFDR method
In this methos, a modulated pulse was transmitted into the beginning of the line (frequency modulated
and amplified chirp pulses), based on the recognition of the reflected pulse beam and measurement of the
time from the generation to the time of the pulse. The thesis will calculate the distance from the beginning of


17

the line to the point of the fault. To distinguish the reflected signal and noise on the line, the thesis use the
correlation function method.
4.2. Chirp signal
A signal whose frequency and amplitude changes over time is called a "chirp". The frequencies of the
chirp signal may vary from low frequency to high frequency or from high frequency to low frequency. The
conversion equation to produce a chirp signal is given by: x (t )  co s(2   f 2 )  cos  2   f ( t )  t   0  in which

k
the frequency varies determined by: f  t   t  f 0 .
2
0.8

Consider a chirp signal with the following

0.6
0.4

parameters:

0.2

 The pulse generator time is   50s .

0
-0.2

 The frequency of pulse generation started with
f 0  400 kH z and increases gradually and

-0.4
-0.6
-0.8
0

ended with the frequency f1  500 kH z .
The initial phase angle  0  0. Amplitude A
changes with frequency

f2 

1
 10 KHz (with
T2

pulse

of

half

generation

time

the

1

2

3
Time(s)

4

5

6
x 10

-5

Figure 4.1: Example chirp signal

cycle

   T2 / 2  50  s ).

Using Simulink to simulate chirp signal with given parameters to obtain chirp signal as shown in Figure 4.1.
4.3 Correlation function
Let x i and y i is the values of the two variables X and Y at times i . Suppose N time i  1, 2, 3, , N . R
is Pearson’s correlation coefficient calculated as in the following formula: R  x, y  

cov( x, y ) cov( x, y)

dx  d y
sx  s y

4.4 Use the correlation function to determine fault location:
4.4.1 Use the correlation function to determine fault location on the transmission lines without
branched:

Figure 4. 2: Simulation model to determine the propagation and reflection wave components on 3-phase lines with
chirp pulse generator

Using the model shown in Fig. 4. 2 when we sent a chirp signal to the beginning of the transmission line,
the signal is measured at the beginning of the line. Figure 4.3 was when there was no fault, Fig 4.4 was when
there was a 3-phase fault at 30km. The correlation function analysis is based on the correlation value of the


18

incoming signal (reference signal sample) with each measured response signal segment, respectively, which

will be graphed as a correlation function as Figs. 4.5 and 4.6.
0.8

0.8
chirp signal
reflect chirp

0.6

0.6

0.4

0.4

0.2

0.2

0

0

-0.2

-0.2

-0.4

-0.4

-0.6

-0.6

-0.8
0

1

2

3
Times

4

5

-0.8
0

6

1

2

-4

x 10

3
Time(s)

4

5

6
-4

x 10

Figure 4.3: Signal measured at the beginning of the line

Figure 4.4: Signal measured at the beginning of the line

when the line is free fault

when the line is three phase fault at 30km.

Let denote X   x1 , x 2 ,  , x N  - a sampled serie of the input chirp signal (with ∆τ = 50ns) with N
values, Y   y1, y2 ,, ym  is the feedback signal measured at the beginning of the line with M value (M

N).

Calculate the correlation values between the sample signal X and the windows (about the same width as X)
consecutively from Y according to the following formula:







j  1,, M  N  1: R j  R X , Y j  R  x1,, xN  ,  y j , y j  N 1 



From there we get the graph of the value of the correlation function between the fault signal and the
feedback signal when there is free fault as shown in Figure 4.5, when a three-phase fault at 30km is shown in
Figure 4.6.
1

1
t1

0.8

t2

0.6

0.5
0.4
0.2

0

0

-0.2
-0.4

-0.5

-0.6
-0.8
-1
0

1000

2000

3000
Time(s)

4000

5000

6000

-1
0

1000

2000

3000
Time(s)

4000

5000

6000

Figure 4.5: Graph of correlation functions between

Figure 4.6: Graph of correlation functions between original

original and feedback signals measured when the line is

and feedback signals measured when the line is three phase

free fault

fault at 30km.

Steps to locate the fault:
Step 1: Send the chirp signal at the beginning
of the transmission line X   x1 , x 2 ,  , x N  ,
measure the reflected signal as Y   y1, y2 ,, ym .
Step 2: Calculate the Ri correlation coefficient
according to the formula (3.59) to obtain:
R   R1 , R 2 ,  , R M  N 1 

R1  R  X ,Y1   R  x1,, xN ,  y1,yN 

R2  R  X ,Y2   R  x1,, xN  , y2 , yN 1 
……………………………………

Figure 4. 7: Algorithm diagram to determine the time of


19
feedback wave



RM  N 1  R  X , YM  N 1   R  x1,, xN  ,  y j , yM 



Bước 3: Find the points with Rj>Rthreshold (Rthreshold = 0.7 for single branch lines). If there existed Rj>Rng
then find the maximum peak Rmax near to Ri. Let tRmax corresponds to Rmax. If there was not Rj>Rthresh except
the one corresponding to the end of the line, then the lines had no fault.
4.4.2 Locate faults on the multi-branch lines
This thesis built a model equivalent to the selected transmission line which is the Lao Cai 110kV
transmission line with parameters of 171 simulation line. in which A is station E 20.2 Lao Cai, C is station E
29.2 Than Uyen, F is station A 20.2 Seo Chong Ho, E is station E29.1 Phong Tho: The segments AB, BC,
BD, DE have the following parameters: l AB  46, 7 km ; lBC  21, 7 km ; lBD  24,8 km; lDE  17 km;
R 0  17, 43 m  / km ; L0  0, 992 mH km ; C 0  11,6452 nF km ; Section DF has parameters: l DF  30, 4 km ;
R 0  14,3 m  / km ; L0  25, 68  H km ; C 0  6, 991  F km ; The transmission system model is shown in

Figure 4.8.

Figure 4. 9: The simulation model identifies the
Figure 4.8: The system of branch transmission lines

propagating and reflecting wave components on a threephase faultless line in the middle of the line

In case the line has many branches as Figure 4.8, When lines have no fault, send a chirp signal at the
beginning of the line (the signal sent from A at the beginning of the line) as shown above will determine the
time t A 0 , t Ai ( i  1  5 ), it is the time when the reflected waves from B, C, D, E, F (the end of the line and
the branch points).
Knowing the time of the pulse generation at the beginning of the line t A0 and t Ai the reflected wave will
be determined (the speed of wave transmission on different segments is different because the line parameters
2 Lij
of the line segments are different). vij 
 i  1...5
j  0...4 where t ji  ti  t j ; l01  l AB ;
t ji

l12  l BC ; l13  l BD ; l34  lDE ; l35  l DF .
When lines have faults, sending the chirp signal to the beginning of the line from A and F. Similar to the
case without faults will determine the time when the value of the large correlation function corresponds to
the time of the wave reflexes from the end of the line or from branches. In addition to these points, if there is
a point, the value of the large correlation function corresponding to the large value of the feedback wave is
t fault .


20

Figure 4.10: Diagram distribution of response time to

Figure 4.11: Diagram distribution of response time to the

the beginning of the line when transmitting from A.

beginning of the line when transmitting from F.

t A0 , t Ai ( i  1..5 ), t Afault is the time of pulse generation from A, the feedback signal from B, C, D, E,
F, from the fault point.

t F 0 , t Fi ( i  1..5 ), t Ffault is the time of pulse generation from F, the feedback signal from D, E, B, D,
A, from the fault point.
 If t Afault  t A1 The fault is in segment AB.
 If t Ffault  t F 1 The fault is in segment DF.
 If t Afault  t Ffault  t F 5  t A 5 The fault is in segment BD.


If t Afault  t Ffault  t F 3  t A1   The fault is in segment BC. Which  is the allowed error

 If t Afault  t Ffault  t F 1  t A 3   The fault is in segment DE.
If the time of the faultt and the fault on which segment was known, fault location will be calculated.
When a fault is on the AB or BC segment, the reflected wave from A will have fewer reflections and
refraction than the reflected wave from F. When the fault is on segment AB or BC, the result of determining
the time of the fault due to the response wave from A will be used.
Similarly, when the fault is on DF, DE, the result of determining the time of the fault due to the
feedback wave from F will be used. Faults on the BD segment may be used to determine the time of the fault
due to reflected waves from A or F.
If the fault is on segment AB, the fault location is
calculated using the following formula:

l fault 
If

the

v01  (t Afault  t A0 )

fault

2
is

l fault  l01 
If

the

fault

is

l fault  l01 
If

the

fault

is

l fault  l35 
If

the

fault

is

on the BC
v12  (t Afault  t A1)

segment:

2
on the BD
v13  (t Afault  t A1)

segment:

2
on the DE
v34  (t Ffault  tF1 )

segment:

2
on

the

DF

segment:

Figure 4.12: Algorithm diagram to identify fault that


21

l fault 

v35  (tFfault  tF 0 )

belong to branch

2

The method of identifying fault locations on branch lines using the inverse correlation function
Sequential calculation steps to determine the value chain of the correlation function:
X   x1 , x2 , , xN  
 X    x N , x N 1 , , x1 
Y   y1 , y 2 , , y N  
 Y    y N , y N 1, , y1 

Call X   x1 , x 2 ,  , x N  - digitized string value of the input chirp signal (within 50ns) with n values

X    xN , xN 1,, x1  , Y   y1, y2 ,, ym  the feedback signal is measured at the end of the line with m
values, Y    ym , ym1,, y1  . Calculate the correlation values between sample signal X ' and windows (about
the same width as X') in succession from Y 'according to the following formula:







to

X    xN , xN 1,, x1 

j  1,m  n  1: R j  R X ,Y j  R  xN ,, x1  ,  y j , y j  n1 
Convert X   x1 , x 2 ,  , x N



and


Y   y1, y2 ,, ym 

to

Y    ym , ym1,, y1  then the feedback signal from the point of fault along the time axis as Figure 4.13.

Figure 4.13: a) Diagram model of the response time wave from fault point b)The model of the
feedback time diagram from the fault point has moved the coordinate axis in the opposite direction.
4.4.3. Some simulation results when using TFDR method

Figure 4.14: Mô hình mô phỏng xác định các thành phần
sóng lan truyền và phản xạ trên đường dây 3 pha có sự cố

Figure 4.15: Mô hình mô phỏng xác định các thành phần
sóng lan truyền và phản xạ trên đường dây 3 pha có sự cố

ở giữa đường dây khi không tải

ở giữa đường dây

The model shown in Figure 4.14 and Figure 4.15 is used to simulate with the following parameter
values of fault:
 Fault simulation model: M = 2 (with load, without load).
 Rfault fault resistance: R = 5 values is (1, 10, 20, 50 ).


22

 Fault inductance: Lfaulf: L = 2 values is (1mH, 10mH).
 Fault location in segments AB, BC, BD, DE, DF. Each line segment selects 2 fault locations. A total
of P = 2x5 = 10 fault locations.
 Fault type: K = 5 types (1 phase fault, 2 phase fault, 2 phase fault to ground and 3 phase fault).
4.4.3.1. Results of calculating line parameters and fault location for non-branch lines
Table 4. 1: Locations of the fault results using the correlation function method
Lfault

Fault type
ABCG
ABC
AG
AB
ABG
ABCG
ABC
AG

AB
ABG
ABCG
ABC
AG
AB
ABG

10km

20km

30km

Coefficient R
0.905
0.944
0.805
0.944
0.874
0.971
0.999
0.815
0.896
0.944
0.971
0.878
0.857
0.878
0.939

L (km)
10.157
10.028
10.145
10.028
10.169
20.150
20.021
19.891
20.009
20.150
30.084
29.955
30.084
29.955
30.084

Error (m)
157
28
145
28
169
150
21
109
9
150
84

45
84
45
84

where R is the correlation coefficient between the line voltage signal and the chirp signal.
The results in Table 4. 1 show that the method applied in the thesis has low errors, the error of the
method is better than the error in [14]. Investigation of fault cases at different locations with different types
of fault, the results show that correlation analysis method can be applied to locate fault for different types of
fault.
4.4.3.2. The result of the system has many branches
When lines don’t fault with the principle circuit diagram as shown in Figure 4.6 and the simulation
model of the process of wave propagation on the multi-branch line as Figure 4. 9. The measured signal result
is shown in Figure 4.16. where t A0 is the time of transmitting the chirp signal into the line, t Ai ( i  1..5 ) is
time of reflected waves from points B, C, D, E, F. tA1 , t A2 are times of the second reflected signal from B
and C.
0.8
0.6

1

t

tA1

t A0

tA2

0.8

A0

A0

t

0.4

t A2

A1

t'A1

t A4

A0

t

0.2

t A4

t A3

t A5

t'A1

0.6
0.4

A3

t

t'

A2

A5

0.2

0

0
-0.2

-0.2

-0.4
-0.4

-0.6
-0.6

-0.8
0

-0.8

0.1

0.2

0.3

0.4

0.5
Times

0.6

0.7

0.8

0.9

1
x 10

-3

-1
0

1000

2000

3000

4000

5000
Time(s)

6000

7000

8000

9000

10000

Figure 4.16: The form of the voltage at the beginning of

Figure 4.17: A graph of the correlation function between

the line when the line is free fault

the input signal and the feedback signal measured when
the line is free fault

Using the correlation function between the fault signal and the feedback signal as shown in subsection
4.2 and running the program as in Appendix 4, the results are shown in the graph as Figure 4.17. In which


23

t A0 is the time of sentting the chirp signal into the line, t Ai ( i  1  5 ) is the time when the reflected waves
from points B, C, D, E, F and, tA1 , t A2 are the times of the second reflected wave from B and C as Figure
4.17.
When lines have fault using the model shown in Figure 4.14, the feedback signal is measured as
Figure 4.18. In addition to the time t A0 and time t Ai ( i  1  5 ) , there is also the time t AF of the time of
feedback pulse from the point of fault. Using the correlation function method above, we can graph the
correlation function between the original signal and the feedback signal when there is a 3-phase on the BC
segment 11 km away from B 11km.
0.8

1

0.6
0.4

0.5

0.2
0

0

-0.2
-0.4

-0.5

-0.6
-0.8
0

0.1

0.2

0.3

0.4

0.5
Times

0.6

0.7

0.8

0.9

1

-1

0

1000

2000

3000

4000

-3

x 10

5000
Time(s)

6000

7000

8000

9000

10000

Figure 4.18: The form of the voltage at the beginning of

Figure 4.19: A graph of the correlation function between the

the line when the line is three phase fault at BC from B

input signal and the feedback signal measured when the line

11km.

is three phase fault at BC from B 11km.

The results calculate the line parameters and fault location
Table 4. 1: The result determines when the wave
response from the beginning of the transmission line
when there is free fault
Feedback
position
B
C
D
E
B 2nd
F

Feedback time Coefficient R
(s)
398,6
0.9897
582,6
0.83835
608,9
0.7055

753,0
0.70373
791,9
0.8347
866,7
0.85

Table 4. 2: Speed of wave on on the segments of
the transmission line
Line
AB
BC
BD
DE
DF

T2( point)
3986
5826
6089
7531
7919
8699

VA (km/s)
234850.3897
234850.3897
234850.3897
234850.3897
233846.1538

VF (km/s)
234850.3897
234850.3897
234850.3897
234850.3897
233846.1538

where VA, VF is the calculated speed according to the feedback wave from A and F, R is the correlation
coefficient between the signal of line voltage and chirp signal calculated according to the formula (4.15).
The response times given in Table 4.2, the application of Equation (4.16) will result in speed tables on line
segments as shown in Table 4. 3.
From the speed of signal values in Table 4. 3 with different simulated cases, calculate according to the
formulas (4.18  4.22) and synthesize the fault location as in the following Table:
Table 4. 3: Calcutation of distance to fault point with
Fault on

AB

BC
BD

three ground phase fault.
Lfault
Coefficient L (km)
R
10
0.905
10.16
20

0.971
20.15
30
0.971
30.08
50
0.757
49.85
55
0.958
54.84
60
0.904
59.80
50
0.757
49.85
55
0.959
54.83

Error
(m)
160
150
8
150
160
200
150

170

Table 4. 4: Calcutation of distance to fault point with one
Fault on

AB

BC
BD

Lfault
10
20
30
50
55
60
50
55

ground phase fault.
Coefficient L (km)
R
0.805
10.14
0.815
19.89
0.857
30.08
0.5

49.84
0.58
54.85
0.56
60.06
0.51
49.84
0.87
54.84

Error(m)
140
110
8
160
150
6
160
160


24
60
35
40
45
15
20
25

DE

DF

0.563
0.79
0.87
0.88
0.969
0.957
0.954

59.79
34.98
39.97
44.75
15.16
20.13
24.82

210
20
30
250
160
130
180

DE

DF

60
35
40
45
15
20
25

0.28
0.54
0.67
0.593
0.819
0.754
0.66

59.79
34.98
39.97
44.75
14.89
20.13
24.82

210
20
30
50

110
130
120

where Lfault is the distance from A to the fault on AB, BC, BD, is the distance from F to the fault on the
DF and DE segments.
Bảng 4. 5: Result of calculating fault location with different resistors
Fault type

Lfault

AG

55 km
BC

ABCG

55 km
BC

Rfault

coefficient R

L(km)

Error (m)

50

100
150
200
250
50
100
150
200
250

0.63
0.61
0.59
0.58
0.58
0.95
0.96
0.96
0.96
0.961

54.85
54.85
54.85
54.85
54.85
54.84
54.84
54.84
54.84

54.84

150
150
150
150
150
160
160
160
160
160

According to the survey results, we find that the method of identifying the fault location on a multibranch line according to the correlation function gives accurate results, high reliability, the number of
measurement points only need from two ends of the line, The method does not require synchronization of
signals from the line heads.
4.5 Conclusion and development
The thesis has studied and built a fault identification model on the transmission line without branches
and multi-branch lines based on the feedback wave analysis method to identify the fault location. The main
contribution of the thesis:
 The thesis has built a simulation model of transmission waves on power transmission lines in case of
faultless lines and in cases of different fault lines.
 The thesis has proposed a model combining wavelet analysis with TSK fuzzy logic neural network to
locate the fault. Which wavelet is used to analyze the feedback signal from the beginning of the line.
Based on the analyzed signal, the instantaneous signal around the time of the changes taking place in the
neural network will be extracted to determine the location of the fault.
 The thesis has built a method of analyzing the correlation function between original wave and feedback
waves to identify the fault location. In which the signal sent to the beginning of the transmission line is a
chirp shaped signal. Especially with power transmission lines with many branches, the thesis has
proposed the method of identifying the fault location with as few measuring devices as possible.

Despite achieving some results as mentioned above, the ideas and proposed solutions still have some
issues that need to be further supplemented and studied, not including the impact of the environment on the
speed of wave propagation and have not detected a few cases of occasional faults.


25

DANH MỤC CÁC CÔNG TRÌNH ĐÃ CÔNG BỐ CỦA LUẬN ÁN

1.An Duong Hoa, Linh Tran Hoai (2016), “Fault detection on the transmission lines using the time domain
reflectometry method basing on the analysis of reflected waveform”, IEEE International Conference on Sustainable
Energy Technologies (ICSET 2016). Hanoi, Vietnam, pp 223-227.
2. Dương Hòa An, Trần Hoài Linh (2015), “Xác định vị trí sự cố trên đường dây truyền tải có nhiều nhánh sử
dụng phương pháp sóng phản hồi chủ động”, Hội nghị toàn quốc lần thứ 3 về Điều khiển và Tự động hóa VCCA 2015,
trang 559-564, Thái Nguyên.
3. Dương Hòa An, Đỗ Trung Hải, Trần Hoài Linh (2016), “Ứng dụng phương pháp sóng phản hồi chủ động và
phân tích hàm tương quan để xác định vị trí sự cố trên đường dây truyền tải”, Tạp chí Khoa học và Công nghệ Thái
Nguyên, Tập 155 - số 10, trang 141-146.
4. An Duong Hoa, Linh Tran Hoai, Hai Do Trung, “An implementation of time-domain reflectometry using
FPGA for transmission lines fault location”, The 11th SEATUC Symposium 2017.
5. Dương Hòa An, Đỗ Trung Hải, Trần Hoài Linh (2019), “Ứng dụng mạng nơron logic mờ để xác định vị trí sự
cố trên đường dây truyền tải”, Tạp chí Nghiên cứu khoa học và công nghệ quân sự, số 10, trang 87-92.