Fault detection through discrete wavelet transform in overhead power transmission lines

Transmission lines are a very important and vulnerable part of the power system. Power supply to the consumers depends on the fault‐free status of transmission lines. If the normal working condition of the power system is disturbed due to faults, the persisting fault of long duration results in financial and economic losses. The fault analysis has an important association with the selection of protective devices and reliability assessment of high‐voltage transmission lines. It is imperative to devise a suitable feature extraction tool for accurate fault detection and classification in transmission lines. Several feature extraction techniques have been used in the past but due to their limitations, that is, for use in stationary signals, limited space in localizing nonstationary signals, and less robustness in case of variations in normal operation conditions. Not suitable for real‐time applications and large calculation time and memory requirements. This research presents a discrete wavelet transform (DWT)‐based novel fault detection technique at different parameters, that is, fault inception and fault resistance with proper selection of mother wavelet. In this study, the feasibility of DWT using MATLAB software has been investigated. It has been concluded from the simulated data that wavelet transform together with an effective classification algorithm can be implemented as an effective tool for real‐time monitoring and accurate fault detection and classification in the transmission lines.


| INTRODUCTION
The power transmission network is an important part of a power system and has a vital role in maintaining the continuity of electrical power to the customers. 1The deregularization of the power sector has forced the utilities to provide uninterruptable power to their customers and resolve power quality concerns promptly. 2he power companies are also looking at reducing the downtime of systems in case of any emergency or abnormal situation. 3The practice of the power operators should be to minimize the fault clearance time so that the system can be brought back into its normal operating state within the minimum possible time. 4n case of any abnormal situation in transmission lines, detection and classification of faults must be as fast as possible so that protective devices can isolate the faulty section to safeguard and protect the power system from damages, such as outages, thermal loading, voltage, angular instability, and so forth. 5Therefore need is to devise a solution that should be able to detect the fault quickly, precisely, and effectively.Faults in transmission can be symmetrical or unsymmetrical and classified as line-line, line-to-ground, three phase fault, and double line-to-ground fault having substantial impact on the performance of transmission lines. 6,7ault analysis has an important association with the selection of protective equipment for the protection and system reliability assessment of extra high-voltage transmission lines.As fault occurs anywhere in the transmission network, the normal working condition of the system is disturbed.If the fault persists for a longer duration it may result in economic losses.Therefore, the fault analysis of 500 kV overhead transmission lines has an important role in ensuring the reliability of the power network in Pakistan.This research will pave the way for analyzing different faults so as to ensure minimum power interruption time, improve mean time to repair, improve time-related to energy not served, and reduce financial losses which is due to sustained power interruption because of faults in overhead transmission lines.
Fault classification in transmission lines needs complex mathematical modeling, signal processing techniques, and expert knowledge to extract features from the fault signal and categorize the type of fault through the implementation of a particular algorithm. 8Several research reveal that certain fault classification algorithms, fault resistance, and fault inception angle, which are essential for exact feature extraction through a selection of suitable signal processing tools have not been considered. 9,10In this study, the DWT has been analyzed to retrieve energy contents in the transient signal at variable parameters, such as changing the location of the fault, changing the fault inception angle, and changing values of fault resistance and ground resistance.These four parameters are not found in the previous work for calculating the energy in the fault signal.The fault in transmission lines creates disturbances and generates current and voltage transients, which are nonstationary in nature and need to be analyzed using time and frequency analysis techniques for fault analysis and diagnosis in power transmission lines. 11,12| LITERATURE REVIEW AND RESEARCH GAP ANALYSIS

| Feature extraction techniques used for fault detection in transmission lines
Various tools used and reported in the past literature for feature extraction from the fault signal with their respective merits and limitations are presented: (1) Fourier Transform (FT) FT actually breaks the input signal into smaller frequencies of different sinusoids. 13This technique is very helpful and simple in nature if the signal is static in nature. 14Conveying accurate information can be challenging for transient or nonstationary signals because certain features may be lost during the conversion from frequency domain to time domain. 15Expression of FT for signal x(t) is as under: x t e dt x t e Which is the inner product of the signal x(t) and the complex sinusoid e j πft − 2 .
(2) Fast Fourier transform (FFT) FFT is a commonly used approach for feature extraction to convert time domain signal into frequency domain. 16FFT with several other algorithms is used by the researchers for fault detection and classification in transmission lines. 17,18The FFT is a useful tool for analyzing stationary signals, and when a signal is periodic, this can be analyzed using the discrete Fourier transform (DFT). 19Given a sequence x(k) of length N, the DFT is defined by.

 X n
x k e n N x k e (2) Research has shown that the STFT is a more effective method for representing a signal in both the frequency and time domains.The STFT is able to overcome the limitations of the Fourier Transform in certain specific cases. 20Among its drawbacks window sizing is an important consideration; once the specific size window is selected, it remains the same for all frequencies. 21Long window does not localize short pulses in the time domain and also low frequencies can hardly be illustrated with a short window. 22,23Equation of a signal x(t) in STFT is given below: X STFT is a function of both time (τspecifies where the window is nonzero) and frequency (f).
(5) Wavelet transform (WT) WT has evolved as a features-extracting tool that overcomes the shortcomings of FT and STFT. 24The WT is capable of providing error-free low-frequency and high-frequency data for long-time intervals, making it a flexible tool for frequency-time transformation with customizable window sizing. 25The WT can analyze fault signals by breaking them down into detailed (cD) and approximate coefficients (cA).This decomposition provides enough information for detecting and classifying faults in transmission lines.Mathematically, a signal x(t) can be expressed in WT as under: m and τ are translating and scale factors.ᴪ(t) is the mother wavelet.Discrete wavelet transform is a type of WT in discrete form, which uses samples of data or discrete signals for analysis of fault signals because of the increasing use and demand of digital relaying in modern power systems, hence digital fault analysis methods rely on DWT. 26 The DWT of a signal x(t) is defined as: where K, m, and n are integers.a m 0 and nb a m 0 0 show scale known as dilation and time shift translation, and parameters b 0 and a 0 are constants.(6) Wavelet packet transform (WPT) WPT uses high-frequency data contained in the faulty signal.To analyze frequency contents, approximate and detailed coefficients are obtained through the decomposition technique. 27The decomposition process takes a lot of time in calculation, so to minimize calculation burden the decomposition is performed up to four levels. 28WPT has the capability to exhibit relatively better frequency resolution than DWT. 29Mathematically, WPT is expressed as: b and a represents wavelet position and scale.ψ n denotes the mother wavelet.(7) Stockwell transform (ST): 1][32] ST possesses capabilities to deliver required information against characteristics of fault signal, that is, time, frequency, and phase angle; it is also prone to noise when used for feature extraction compared with other counterpart signal processing techniques.S transform for signal x(t) is mathematically expressed as: t and f specify time and frequency and Τ is control parameter used for Gaussian window adjustment.A comparative analysis of the mentioned featured extraction tools is shown in Table 1.
It is revealed that DWT is the most effective tool for analyzing the transient signal to extract its features for fault detection.DWT is able to handle the impacts of various parameters, such as fault inception angle, fault resistance, ground resistance, and fault location in fault detection for transmission lines.These parameters can affect the spectral energy needed for feature extraction from the fault signal, and in turn, affect the accuracy of | 4185 fault detection.A summary of the literature review of the previous work carried out by the researchers is presented in Table 2; it highlights the details about feature extraction tools and fault classification techniques along with details of parameters considered by the researchers in their respective research work.Whereas this study considers all the parameters for fault detection against the previous work, which is lacking due to some or few parameters considered for fault detection.Considering all these parameters and analyzing faults through MATLAB/SIMULINK, this study reveals the validity of results in terms of identifying faulty phases using DWT as a feature extraction tool to achieve novel results.

| RESEARCH METHODOLOGY
Fault signals considering various parameters, that is, fault inception angles, fault resistance, fault resistance, and ground resistance are generated in transmission lines using DWT as a feature extraction tool, which has been widely used by researchers for fault detection due to its inherent characteristics to overcome effects of noise in detection of fault and understating information in both time and frequency domain. 48,49The methodology used in this work can be understood from the following steps and flow chart, as shown in Figure 1.■ MATLAB/SIMULINK has been used for modeling and simulation due to its characteristics, such as high accuracy, reliability, easiness of implementation, and fastness.■ Use of MATLAB code to find out DWT coefficients.■ Obtaining detailed and approximate coefficients at level 4 to obtain the fault index value.■ Differentiate between fault and normal state of the system based upon fault index value compared to a suitable threshold value.

| Single-line diagram of proposed research work for fault detection
A single-line diagram of a transmission line under study along with length and sources is shown in Figures 2 and 3, based upon real data of an operational section of a 500 kV transmission line between Jamshoro-New Karachi, Sindh, Pakistan.Table 3 describes the total length of the 500 kV transmission line section under study along with normal power handling capacity per circuit, thermal loading of power in MW, type, and configuration of the conductor.Table 4 details the electrical parameters of a source and line parameters of an existing 500 kV transmission line between Jamshoro-New Karachi (Sindh, Pakistan), along with the conventional frequency used in the national grid of Pakistan.The fault duration window is 1 s used for fault simulation.A MATLAB model of the same 500 kV transmission line circuit of 155 km length between Jamshoro-New Karachi, Sindh, Pakistan, has been developed.The model comprises two sections, each having a distance of 100 and 55 km, respectively, at different parameters as mentioned in Table 5.

| MATLAB model of the 500 kV transmission line based on actual parameters for fault detection and classification
A MATLAB model of the transmission line has been built using MATLAB version 2020 as shown in Figure 4   parameters considered are completed for all different types of faults as mentioned in Table 6.
The fault signals, that is, currents contains high frequency component that need to be analyzed for fault detection in transmission lines. 50,51The previous research reveals that wavelets are effectively used for analyzing transients in the fault signals. 52Use of multiresolution analysis (MRA) as the tool which decomposes the original signal into approximate and details, that is, to low frequency signal and high frequency through wavelet transforms. 53To obtain approximate and detailed coefficients the signal is passed through a high pass and low pass, detailed process showing how does detailed and approximate coefficients are obtained is shown Figure 5.
A sampling frequency of 20 kHz has been used in this research work as it provides a number of benefits, such as more accurate fault detection and identification, the ability to capture high-frequency components of fault signals, and reduced risk of aliasing.For MRA analysis, the signal is passed through high pass and low pass filters for disseminating it further into two for obtaining detailed and approximate coefficients, the cycle is repeated, and the signal is decomposed further until it arrives at the predicted level.Mother wavelet Db4 has been chosen for level 3 decomposition due to its proven feature extraction characteristics, the original frequency of the fault signal is captured by detail coefficients (cD) D1, D2, T A B L E System data and line parameters of 500 kV transmission line between Jamshoro-New Karachi.D3, D4 and approximate coefficient (cA) up to level A4.This helps in extracting useful information from the original signal into different frequency bands. 546][57] The wavelet toolbox in MATLAB is the tool for wavelet analysis; Figures 6  and 7 explain the whole decomposition process.

S # Entity
From the fault analysis and the values of the coefficients obtained analytically, it has been cleared that either the fault is in phase(s) with or without ground, the values of coefficient (spectral energy content) are seen quite high in faulty lines as compared to healthy lines.The following formula is used for extracting spectral energy from the signal using WT 58 : | 4189 where E is the spectral energy, n, k, j and detailed coefficients (cD) is the coefficient number, window's number, and the wavelet decomposition level and the magnitude of the coefficient for the details from WT, respectively.Each spectral energy data contains the energy during a certain window length. 59ault impedance affects phases and ground mode energies E WTC = 2 which is less when fault impedance is high and vice versa.Energy content distinguishes between the normal and faulty phases. 16Fault inception angle at which fault transients occur in voltage and current are square sinusoidal functions of the wavelet coefficients. 60ables 7, 8, and 9 show the magnitude of coefficients for various fault types at different variables, that is, fault resistance, ground resistance, fault inception angle, and lengths at which fault occurs in transmission lines.

| SIMULATION RESULTS AND ANALYSIS
The fault current during each fault generated using variable parameters, as specified in Table 4 (see Section 3.1), is shown in output waves in Figures 8 and 9.
Following is the summary of the final findings in the context of the behavior of fault current and subsequent energy contents in the transient signal, Table 10.Since the MATLAB model has been simulated by changing the various parameters.From the simulated results, it has been observed that by incorporating the mentioned parameters and their variation, it is understood that: • The fault resistance affects high impedance faults (HIFs) since phases and ground mode energies E WTC = 2 peaks are smaller in high resistance faults than low impedance faults, which result in smaller wavelet energies.• The faults involving ground resistance can also cause incorrect signal measurement data • The fault inception angle affects the severity of the fault-initiated traveling waves.• As the impedance is proportional to the distance between the fault point and the relay, the relay indirectly indicates the distance and location of the fault.
Besides the results, variation of the fault current can also be measured in the form of energy content in the transient signal as its fault index compared with certain threshold values is considered fixed for relative comparison.Based upon the net energy content of the faulty phase(s) with or without ground, it is easy to distinguish between faulty and healthy states of the power transmission network.This validates that even with changing variables, feature extraction from the fault signal is not affected.Therefore it is concluded that DWT is robust and variations of input parameters in the MATLAB model do not affect the energy of the signal during the fault.
As discussed earlier, the energy contents in the fault signal also vary in accordance with the change in fault inception angle, which is helpful for the accurate detection of fault by extracting features from the fault signal.Figure 10 helps to understand the behavior of T A B L E 7 Maximum values of coefficients in different phases and ground according to the type of fault at fault resistance R f = 0.001 ohm, ground resistance R g = 0.01 ohm, fault inception angle (FIA) = 30⁰, and length at which fault occurred = 10 km.  12 No fault Under normal conditions (no-fault situation), when there is no fault in the transmission line, no variation in phase current has been observed, as shown in Figure 9F, hence the normal state of the power system is maintained.

Max coeff of
showing the process of feature extraction from fault signal for fault detection and fault classification in transmission lines.
relevant parameters in each block are adjusted like line parameters in section blocks, the setting of fault type in fault block along with a change of fault inception angle, fault resistance, ground resistance and location of transmission line in source, fault, and transmission line section blocks, respectively.Thus the process of simulation is initiated and continued till all possible combinations of selected values of F I G U R E 2 Block diagram showing the process of feature extraction from the fault signal.F I G U R E 3 Single line diagram of the 500 kV transmission line (Jamshoro-New Karachi, Pakistan).T A B L E 3 Data of model under review (500 kV Jamshoro-New Karachi Circuit).
Nomenclature of different types of faults.E 5 analysis (MRA) in DWT for feature extraction.F I G U R E 6 Three-level DWT decomposition of a faulty phase current.AHMED ET AL.

F I G U R E 7
Three-level DWT-based decomposition of phase current, showing approximate (cA) and detailed coefficients (cD) for feature extraction from fault signal.

F
I G U R E 8 Current waveforms during AG, BG, CG, ABG, BCG, and ACG faults.(A) Current waveform during AG fault.(B) Current waveform during BG fault.(C) Current waveform during CG fault.(D) Current waveform during ABG fault.(E) Current waveform during BCG fault.(F) Current waveform during ACG fault.T A B L E 10 Summary of the simulation results.S # Type of fault Conclusion 1 Phase A to ground fault During the AG fault in the transmission line, there seems an abrupt rise in the fault current in phase A, as shown in Figure 8A. 2 Phase B to ground fault During the fault in phase B with ground (BG) in the transmission line, the raised value of current in phase B is shown in Figure 8B. 3 Phase C to ground fault Under the CG fault (fault in phase C with respect to ground) the variation in the amplitude of current in phase "C" during the fault is shown in Figure 8C. 4 Line to Line with ground fault (ABG) Under the ABG fault, an abrupt rise of fault current in phases A and B is noted, which has been shown in Figure 8D. 5 Line to Line with ground fault (BCG) Under BCG fault, as shown in Figure 8E, fault has occurred in two phases, that is, B & C with an abrupt rise of fault current in respective phases B and C. 6 Line to Line with ground fault (ACG) Under double line to ground fault, as shown in Figure 8F, fault has occurred in phases A & C of the transmission line with respect to ground; it is observed that fault current in faulty phases attained their normal values.7 Line to Line fault (AB) Under an unsymmetrical fault that has occurred in between phases A and B, the magnitude of fault current in respective phases is quite high, which can be seen as shown in Figure 9A.8 Line to Line fault (BC) During the double phase fault between phase B and phase C fault, the rise of current is shown in respective faulty phases, as shown in Figure 9B.9 Line to Line fault (AC) Under the AC fault, a fault has occurred in between phases A and C, the wave output in Figure 9C shows the variation of fault current in those faulty phases.10 Symmetrical fault ABC Under the symmetrical fault ABC, the behavior of current in each phase is shown in Figure 9D, which shows an amplitude variation of current in each phase of the transmission line.11 Symmetrical fault ABC with ground Under the ABCG fault, amplitude variation in current in each phase of the transmission line has been observed, as shown in Figure 9E.

F I G U R E 10
Transient response of fault signal during unsymmetrical fault, that is, ABG at different fault inception angles.(A) and (B) Transient response of fault signal at FIA = 0°and 10°during ABG fault.(C) and (D) Transient response of fault signal at FIA = 20°and 30°during ABG fault.(E) and (F) Transient response of fault signal at FIA = 40°and 50°during ABG fault.(G) and (H) Transient response of fault signal at FIA = 60°and 70°during ABG fault.(I) and (J) Transient response of fault signal at FIA = 80°and 90°during ABG fault.

1
Limitations of feature extraction techniques used for fault detection in transmission lines.Summary of the literature review.
Its conversion in time and frequency domain for fault analysis in power transmission lines is easy.FFT does not provide information in the time domain whereas the computation of the faulty or transient signal is required in the frequency domain.It provides an accurate assessment of stationary signals.Wavelet packet transform (WPT)It provides better time-frequency resolution than the Fourier transform and wavelet transform and also has high flexibility.Computational complexityDifficulty in selecting the appropriate wavelet and decomposition level.Sensitivity to noise.T A B L E 2 Maximum values of coefficients in different phases and ground according to the type of fault at fault resistance R f = 10 ohm, ground resistance R g = 2 ohms, fault inception angle (FIA) = 90⁰, and location of fault at length = 100 km.