Abstractâ This paper presents a comparative study of the performance of Fourier transform and wavelet transform based methods for detection, classification ...
A Comparison of Fourier Transform and Wavelet Transform Methods for Detection and Classification of Faults on Transmission Lines D.Das, N.K.Singh, and A.K.Sinha, Member, IEEE
Abstract— This paper presents a comparative study of the performance of Fourier transform and wavelet transform based methods for detection, classification and location of faults on high voltage transmission lines. The algorithms devised are based on Fourier transform analysis of transient current signals recorded in the event of a short circuit on a transmission line. Similar analysis is performed using multi-resolution Daubchies-8 wavelet transform and comparative merits of the two methods are discussed. Index Terms—Discrete Fourier Transforms, Power Transmission Faults, Power Transmission lines, Wavelet Transforms.
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I. INTRODUCTION
HORT circuit faults on transmission lines occur due to several reasons. A majority of these are caused by lightning strike (direct or indirect) while some other causes are a tree branch shorting the transmission line etc. Some of these short circuits cause permanent damage to the line insulators (insulators cracking due to heavy flashover etc.) and/or line conductors. It is necessary to identify and accurately locate the fault so that the repair could be carried out quickly to bring the line back in service as soon as possible. The occurrence of any transmission line fault gives rise to a transient condition. The transient phase is marked by the presence of harmonic currents. Transforms are used in order to extract information about these harmonics. Fourier transforms [8] and wavelet transforms [12-14] are two major tools that are used for frequency domain analysis of any signal. While Fourier transform gives us information about all the frequencies present in the signal it gives no indication as to when in time were these signals present. Wavelet transform give us multi-resolution analysis in time and frequency i.e. for higher frequencies we can get better time resolution then for lower frequencies. Although a number of studies have been conducted independently on using Wavelet [1-3, 9-11] and Fourier
Transforms [5] for fault detection and classification, their performances have not been compared. It is important to know which method should be applied for which purpose in order to get the best possible result. This paper is an attempt to answer to the above problem has been discussed. II. DETECTION AND CLASSIFICATION OF FAULTS In the recent past a lot of studies have been carried on detection and classification of faults on transmission lines using various DSP techniques [8]. Fourier transform being one of the basic tools of DSP and also one of the simplest one is often used for this purpose [5]. Being a multi-resolution technique wavelet has become considerably popular in the recent years [1-3, 9-11]. A. Discrete Wavelet Transform In this paper Discrete Wavelet Transform (DWT) has been used for detecting and classifying faults on transmission lines. The technique used is similar to one used in [1]. A filter bank model for obtaining the DWT coefficients for a sampled signal with 512 (29) samples is shown in Fig. 1.
D.Das, N.K.Singh, and A.K.Sinha are with Electrical Engineering Department, Indian Institute of Technology, Kharagpur, India.
0-7803-9525-5/06/$20.00 ©2006 IEEE.
Fig. 1. Filter bank model of DWT for 512 samples, sampled at 80 µs
(For integer states upto n levels 2 n samples are needed) [4]. For detection and classification of faults on transmission lines different types of faults at different locations on the line were simulated and their current signals were sampled at regular intervals of time. For the purpose of analysis 512 samples sampled at 80µ seconds were used. These 512 (6.25 kHz) samples are passed through a high pass (g[n]) and a low pass (h[n]) filter respectively to get 256 samples each (Fig. 1). Now the lower 256 (6.25 kHz) samples are further passed through a high pass and a low pass filter respectively. The low pass filters here give us the coefficients for the wavelet transform. This process continues till the 3rd level when the high pass filter gives the frequency range 97.65Hz – 195.3Hz i.e. a range consisting of 2nd as well as third harmonic frequencies which are most prominent in fault current signal. The DWT coefficients for Daubechies-8 wavelet corresponding to this level for the three phase currents are used in the analysis. For detection and classification using DWT a few parameters are defined as given below: Sa= Summation of 3rd level coefficients for phase A. Sb= Summation of 3rd level coefficients for phase B. Sc= Summation of 3rd level coefficients for phase C. The parameters Qa, Qb and Qc are defined as: Qa= Summation of absolute values of 3rd level coefficients for phase A. Qb= Summation of absolute values of 3rd level coefficients for phase B. Qc= Summation of absolute values of 3rd level coefficients for phase C. The ratios P1, P2 and P3 are defined as: P1=Qa/Qb, P2=Qb/Qc and P3=Qc/Qa. Qth is defined as a threshold value, which can be taken as max(Qa, Qb, Qc) for the maximum safe value of current through the transmission line. The algorithm for the classification of faults using DWT is given in Fig. 2. The criterion for classification as LLL fault is same as given in [1]. However the criteria for the other faults were modified. In [1] for the purpose of fault classification the ratios Z1, Z2, Z3 were defined as: Z1=Sa/Sb, Z2=Sb/Sc and Z3=Sc/Sa and the criterion used for classification as LLG fault, was none of the three ratios Z1, Z2, Z3 is equal to one. While for LG fault the criterion was that one of them should be equal to one while the next one in cyclic order should be less than one. However, the simulation results show that the performance of these criteria were not very good. Hence to improve the performance of the fault classification algorithm, the algorithm was modified as shown in Fig. 2. This gave better results. B. Discrete Fourier Transform The method for classifying faults using DFT is formulated on a similar line. In the method using FFT algorithm, first the DFT of the current signals in the three phases is found. The amplitude of the component corresponding to 50Hz (fundamental) is taken. Let these amplitudes in the three lines be termed A50, B50 and C50. The ratios R1, R2 and R3 are
defined as: R1=A50/B50, R2=B50/C50 and R3=C50/A50. BEGIN
Determine Sa, Sb, Sc, Qa, Qb and Qc
Is Sa+Sb+Sc=0 ?
P1=1 && P2>1 Or P2=1 && P3>1 Or P3=1 &&P1>1
Only one among Qa, Qb and Qc >Qth?
LLL fault
LL fault
LG fault
LLG fault Fig. 2. Fault classification algorithm using DWT
Ath is defined as a threshold value, which can be taken as max(A50, B50, C50) for the maximum safe value of current through the transmission line. The complete algorithm used for classification of faults on transmission lines using DFT is shown in Fig. 3. Using DFT it was not possible to correctly distinguish between LL and LLG faults as the ratios overlap for most of the cases. Simulation Details: The simulations were done on a simple transmission line circuit consisting of a generator at one end and a R-L load at
the other end. The base values of the voltage and the power in the system are 400kV and 100MVA.
BEGIN
circuit is simulated and the data are recorded. The transforms (both DWT and DFT) are found using 512 samples. The total duration of the analysis comes out to 512*80µs = 40.96ms, which is about 2 cycles of a 50Hz system. “SimPowerSystems” package of Matlab is used for simulation. The circuit used in simulation is shown in Fig. 4.
Determine R1, R2, R3
Is R1=R2=R3=1 ?
L O A D
LLL fault
Fig. 4. Simulation Model
Only 1 among A50, B50 and C50 > Ath
LG fault
C. Results and Discussions: The results of the simulations using DWT are presented in Tables I, II, III and IV. TABLE I VALUES OF SA, SB , SC AND SA+SB+SC IN CASE OF LLL FAULT AT A DISTANCE OF 25KM
LL fault or LLG fault
Fig. 3. Fault classification algorithm using DFT
The frequency of the system is 50Hz. The total impedance of the generator and transformer taken together is (0.2+j4.49) Ω. The transmission line parameters in terms of positive negative and zero sequence parameters are: A) Resistance per unit length: positive sequence = negative sequence=0.02336 ohms/km; zerosequence=0.38848 ohms/ km B) Inductance per unit length: positive sequence = negative sequence= 0.95102 mH/km; zerosequence=3.25083 mH/km C) Capacitance per unit length: positive sequence = negative sequence = 12.37 nF/ km; Zero-sequence=8.45 nF/ km The load impedance is 720 + j1.111 corresponding to a load of 200MVA at a power factor of 0.9 lagging. The sampling time for the system was taken to be 80µ seconds. It is a 300 km line and the location of fault is varied over the length of the line at an interval of 10Kms. A low resistance fault with fault resistance of 0.04 Ω is simulated. For each location the fault inception angle is varied from 0° to 180° in steps of 10°. For each value of inception angle the faulted
Inception Angle 0 80 150 170
Sa -23167 -31069 6972 18748
Sb 35539 -365 -34150 -36078
Sc -12372 31433 27178 17331
Sa+Sb+Sc 0 0 0 0
TABLE II RANGE OF VALUES OF QA, QB AND QC FOR LG FAULT ON PHASE A AT A DISTANCE OF 295KM Inception Angle 20 80 140 170
Qa 1.83E+05 8.88E+04 1.10E+05 1.67E+05
Qb 1.77E+04 2.20E+04 8.21E+03 9.68E+03
Qc 2.70E+04 1.19E+04 3.37E+04 3.45E+04
TABLE III RANGE OF VALUES OF P1, P2 AND P3 FOR ALL VALUES OF DISTANCES AND INCEPTION ANGLE IN CASE OF LL FAULT ON PHASE A-B Max Min
P1 1.198935 1.007305
P2 92.44997 4.668632
P3 0.178945 0.010718
TABLE IV RANGE OF VALUES OF P1, P2 AND P3 FOR ALL VALUES OF DISTANCES AND INCEPTION ANGLE IN CASE OF LLG FAULT ON PHASE A-B AND GROUND Max Min
P1 2.043121 0.584554
P2 54.31541 5.933887
P3 0.210716 0.00988
As can be seen from Table I, in case of an LLL fault the quantity Sa+Sb+Sc=0. In case of LG fault, a suitable value of Qth is chosen. For example from Table II, Qth can be chosen to be 6.4E+4, which is twice the maximum value of Q under healthy condition. The condition for LL fault is chosen as 1
