-1- INTRODUCTION 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 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 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 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 1: Single-phase  transmission line model Fig 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 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  and   V ref  Z  Z    Z0  Z 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 Z  Z0   ref  Z0  Z Vinc Z  Z 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  tl  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 Vinc Rt  Z 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 )   Vinc   e   Rt  Z R  Z  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 )   Vinc  *e   R  Z1  where: T  R  Z1 L R  Z1 Fig 2.7: Equivalent Petersen model for lines with R-L 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 )   Vinc   (1  e T )   Rt  Z  where: T  Rt  Z0  Ct time coefficient When t=0 has Rt  Z Fig 2.8: Equivalent Petersen model for lines with RC parallel load Vtd (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    e  Rt  Z   Fig 2.9: Equivalent Petersen model for lines with R-C serie load where T  ( R  Z )  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 Z 0  Z 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  1Vinc  Z0  Vinc  Z fault  Z And refractive components spread to the end of transmission line as: 1   1 Vinc  (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 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 11: Block diagram to identify fault locations on the transmission lines 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 12 Fig 12: Model of simulating wave propagationon the transmission lines 2.3.2 Building elements used in the simulation Fig 13: Block diagrams simulating fault forms, DC Fig 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 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: 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 ( t )  d ( 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:  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 (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 0.8 0.5 0.6 0.4 0.2 -0.5 -1 -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 -0.8 -0.1 -1 100 0.2 100 200 300 400 500 600 700 800 900 1000 Fig 3.3: Signal of function y(t) -0.2 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 =~ 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 (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 30 -10 20 -20 10 0 -30 0.5 1.5 2.5 3.5 4.5 -400 Time(s) x 10 0.5 1.5 -3 2.5 3.5 Times(s) 4.5 x 10 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 -1 -2 -3 -4 -5 0.5 1.5 2.5 3.5 Times(s) 4.5 x 10 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  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  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  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    / If   0.025 then go back to step 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 corresponds to the time of closing the pulse generator (in this thesis, it is chosen at 2ms): t0  d1 (t )   where   0,1; t  ms The location of the fault point (if it exists) will be t t t calculated by formula: x  v   v  where: 2 v  wave speed on the transmission line, mean as: v 2l where T0  t0 T0  t 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 3.1 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 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 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, km ; lBC  21, km ; lBD  24,8 km; lDE  17 km; R  17, 43 m  / km ; L0  0, 992 mH km ; C  11,6452 nF km ; Section DF has parameters: l DF  30, km ; R  14,3 m  / km ; L0  25, 68  H km ; C  6, 991  F km ; The transmission system model is shown in Figure 4.8 Figure 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 , t Ai ( i   ), 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 Lij of the line segments are different) vij   i  j  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  ), 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 , t Fi ( i  ), 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 The fault is in segment DF  If t Afault  t Ffault  t F  t A The fault is in segment BD  If t Afault  t Ffault  t F  t A1   The fault is in segment BC Which  is the allowed error  If t Afault  t Ffault  t F  t A   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 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: on the BD v13  (t Afault  t A1) segment: on the DE v34  (t Ffault  tF1 ) segment: on the DF segment: Figure 4.12: Algorithm diagram to identify fault that 21 l fault  v35  (tFfault  tF ) belong to branch 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 , , y N    Y    y N , y N 1, , y1  Call X   x1 , x ,  , 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 ,  , 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: Mơ hình mơ xác định thành phần sóng lan truyền phản xạ đường dây pha có cố Figure 4.15: Mơ hình mơ xác định thành phần sóng lan truyền phản xạ đường dây pha có cố đường dây không tải 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 = (with load, without load)  Rfault fault resistance: R = values is (1, 10, 20, 50 ) 22  Fault inductance: Lfaulf: L = values is (1mH, 10mH)  Fault location in segments AB, BC, BD, DE, DF Each line segment selects fault locations A total of P = 2x5 = 10 fault locations  Fault type: K = types (1 phase fault, phase fault, phase fault to ground and phase fault) 4.4.3.1 Results of calculating line parameters and fault location for non-branch lines Table 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 21 109 150 84 45 84 45 84 where R is the correlation coefficient between the line voltage signal and the chirp signal The results in Table 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 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  ) 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 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 -0.2 -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8 0.1 0.2 0.3 0.4 0.5 Times 0.6 0.7 0.8 0.9 x 10 -3 -1 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   ) 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   ) , 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 0.6 0.4 0.5 0.2 0 -0.2 -0.4 -0.5 -0.6 -0.8 0.1 0.2 0.3 0.4 0.5 Times 0.6 0.7 0.8 0.9 -1 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 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 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 From the speed of signal values in Table with different simulated cases, calculate according to the formulas (4.18  4.22) and synthesize the fault location as in the following Table: Table 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) 160 150 150 160 200 150 170 Table 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) 140 110 160 150 160 160 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 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 CƠNG TRÌNH ĐÃ CƠNG 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 Dương Hịa An, Trần Hồi Linh (2015), “Xác định vị trí cố đường dây truyền tải có nhiều nhánh sử dụng phương pháp sóng phản hồi chủ động”, Hội nghị toàn quốc lần thứ Điều khiển Tự động hóa VCCA 2015, trang 559-564, Thái Nguyên Dương Hòa An, Đỗ Trung Hải, Trần Hồi Linh (2016), “Ứng dụng phương pháp sóng phản hồi chủ động phân tích hàm tương quan để xác định vị trí cố đường dây truyền tải”, Tạp chí Khoa học Cơng nghệ Thái Ngun, Tập 155 - số 10, trang 141-146 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 Dương Hòa An, Đỗ Trung Hải, Trần Hoài Linh (2019), “Ứng dụng mạng nơron logic mờ để xác định vị trí cố đường dây truyền tải”, Tạp chí Nghiên cứu khoa học cơng nghệ quân sự, số 10, trang 87-92  ... định thành phần sóng lan truyền phản xạ đường dây pha có cố Figure 4.15: Mơ hình mơ xác định thành phần sóng lan truyền phản xạ đường dây pha có cố đường dây không tải đường dây The model shown in... An, Đỗ Trung Hải, Trần Hồi Linh (2019), ? ?Ứng dụng mạng nơron logic mờ để xác định vị trí cố đường dây truyền tải? ??, Tạp chí Nghiên cứu khoa học cơng nghệ qn sự, số 10, trang 87-92 ... An, Đỗ Trung Hải, Trần Hồi Linh (2016), ? ?Ứng dụng phương pháp sóng phản hồi chủ động phân tích hàm tương quan để xác định vị trí cố đường dây truyền tải? ??, Tạp chí Khoa học Công nghệ Thái Nguyên,