-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
2l
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(xA2
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(xA1
X
W(xA
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 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
- Xem thêm -
.PDF 
25 
16 
56 
