A multivariable transmission line protection scheme using signal processing techniques

This paper introduced an advanced algorithm making hybrid use of Stockwell transform (ST), Hilbert transform (HT) and Alienation coefﬁcient (ACF) for identiﬁcation, classiﬁ-cation and to locate faulty events on transmission line. Signals of Current are processed by application of ST, HT and ACF for computing S-index, H-index and A-index, respectively. These indices are multiplied element by element to compute proposed fault index (FI). A threshold magnitude is decided after testing the algorithm during different fault scenarios and faulty events are recognized when FI exceeds this threshold magnitude. Faults are categorized by identifying the number of phases which are faulty in nature and a ground fault index (GFI). GFI is designed by processing the zero sequence current using ST and used to identify involvement of ground during fault event. A mathematical formulation is framed to estimate location of faults on transmission line. Fault location has been estimated with a mean error less than 1%. Investigated faults include phase to ground (PGF), double phase (PPF), double phase to ground (PPGF) and three phase to ground (TPGF). Algorithm is found effective for faulty scenario such as fault impedance variations, fault incidence angle (FIA) variations, reverse power ﬂow, effect of line loading, effect of noise, transient faults, off-nominal frequency, and presence of harmonic components. Algorithm is also effective for discriminating switching transients from faulty conditions. Effective performance of the algorithm is established by comparing with fault detection and classi-ﬁcation approach based on alienation coefﬁcients, discrete Fourier transform (DFT) and time-frequency approach. Study is performed on a two terminal transmission line in MAT-LAB/Simulink environment. Effectiveness of the algorithm is also established on a real time transmission grid of Rajasthan state of India.


INTRODUCTION
Faulty events such as phase to ground (PGF), double phase (PPF), double phase to ground (PPGF) and three phase to ground (TPGF) incident on the transmission line cause mechanical stress, excessive heating of components and produce unbalance current in the utility network. Hence, it is desired to trip the transmission line as soon as fault event is observed. This can be achieved using fault detection, classification and estimation algorithm (FDCEA) based protection relays. Efficient FDCEA reduces restoration cost of principal components analysis (PCA), rule based decision tree (RBDT), empirical mode decomposition (EMD) etc. [2]. A protection scheme for uncompensated transmission line by processing the current signals using Wavelet Transform (WT) and Chebyshev Neural Network (ChNN) is reported in [3]. This has advantages of improved protection speed and efficiency.
In [4], authors designed a protection scheme for transmission line which is fast and reliable in nature and based on the use of Euclidean distance between samples and processing current signals using discrete Fourier transform (DFT). Algorithm effectively identifies the symmetrical and unsymmetrical faults during scenario of variable fault inception angle (FIA) and fault resistance. It is effective to identify fault type and location on transmission line. A technique using combination of the co-variance of current signals with a cumulative technique for recognition of faults on transmission lines in conditions of power swings is reported in [5]. Algorithm effectively identifies fault locations, faults with variable impedance, and different times of fault inception. Algorithm is also effective to identify faulty events during different loading angles, sudden change of load, and reversal in power flow direction. Amit et al. [6], presented KMC and weighted KNN regression based hybrid method for recognition of faults on transmission line. Algorithm is effective for identification of fault events in various cases of study and noisy environment. A wavelet transform, neural network and ACF based techniques for identification and location of faults on uncompensated transmission line and line compensated by Unified Power Flow Controller (UPFC) is reported in [7], [8]. Algorithm effectively recognizes transmission line faults at various locations on the line, different sampling frequency, system parameters, noisy environment, different FIA, and different control approaches. A technique using ST and WDF which is effective to provide protection to power transmission line during different operating conditions such as variations in FIA, fault impedance, and loading condition is reported in [9]. Algorithm effectively discriminates the faulty and switching events. In [10], authors introduced an ACF and WDF supported protection scheme for network of power system where Renewable Energy (RE) penetration is high. A method based on monitoring the positive sequence voltage and currents for identifying the fault direction on transmission line equipped with a series compensator is reported in [11]. This method has the merits that it does not require high sampling frequency, performance is not affected by current inversion and voltage inversion, and method is simplified in nature so that it can be easily implemented. In [12], authors designed an algorithm for distance protection of transmission line using the fast discrete ST. This is effective to detect all types of faults with large number of power electronics based generators. An approach to recognize faults on the transmission line using graph convolution network (GCNN) is introduced by authors in [13]. It observed that the proposed approach has strong feature extraction capability which improves the fault identification efficiency of the algorithm. After detailed analysis of literature reviews discussed, it is established that hybrid combination of two or more signal processing techniques and intelligent techniques will improve the performance of protection schemes. Hence, this paper has considered hybrid application of ST, HT and ACF for design of a transmission line protection scheme. Main research contributions of this paper are briefly discussed below:-• A new current based algorithm which makes hybrid use of ST, HT and ACF is designed which is effective for identification, classification and to locate faults on power transmission line. • A FI is proposed which effectively discriminates the faulty and healthy conditions by a simple comparison of peak magnitude with a threshold magnitude. • Faults are classified using number of faulty phases and a GFI.
GFI is computed by decomposing the zero sequence current using ST and used to identify involvement of ground during fault event. • A mathematical formulation is designed to estimate fault location on transmission line. Algorithm is effective to locate faults on transmission line with a mean error less than 1%. • Algorithm effectively identifies faulty events with variations in fault impedance, reverse power flow, fault incidence angle (FIA), effect of line loading, effect of noise, transient faults, off-nominal frequency, and presence of harmonic components. • Algorithm effectively discriminates switching transients from the faulty conditions. • Algorithm effectively identifies and locates the faults on a real time transmission utility grid.
This paper is organized in ten sections. Section 1 includes introduction and contribution of research. Test transmission line and related data are described in Section 2. All steps of proposed transmission line fault detection, classification and estimation algorithm are illustrated in Section 3. Transmission line fault detection and classification results are elaborated in Section 4. Results related to different case studies are discussed in Section 5 whereas results for differentiating the operational events from fault events have been discussed in Section 6. Fault estimation results are discussed in Section 7. Results to test the performance of algorithm on a real time transmission network are discussed in Section 8. Performance comparative study is elaborated in Section 9 and concluding remark is detailed in Section 10.

TEST TRANSMISSION LINE
Performance of algorithm is tested on a transmission line which has two terminals and described in Figure 1. core. Details of CT constructions, saturation of core and testing are available in [14][15][16]. In simulation study it is realized by the use of V-I measurement block placed on bus-1 of test transmission line. The current recorded using CT is processed applying the algorithm for continuous monitoring of health of the power test transmission line. If a fault scenario is observed, then a trip command will be generated for the circuit breaker (CB-2) to trip the line. Similar arrangement may be installed near bus-2 for tripping the line from receiving terminal so that whole transmission line may be isolated from the system during faulty conditions. Transmission line parameters reported in [7] are used in this study and included in Table 1. Fault events are simulated at center of the transmission line.

PROPOSED ALGORITHM FOR TRANSMISSION LINE PROTECTION SCHEME
This section describes the proposed transmission line protection algorithm which detects, classifies and locates the faults incident on the transmission line. A flow chart indicating all the steps of the proposed protection algorithm is illustrated in Figure 2.

Transmission line fault detection and classification
A FI is designed to detect fault events occurring on the transmission line. This fault index is computed using the H-index, S-index and A-index which are described in this section. Classification of faulty events is realized by identifying the number of faulty nature phases. Involvement of ground during fault events is identified by application of a GFI which is described in this section.

H-index
Recorded current signals are processed using the HT using sampling frequency equal to 3.84kHz. HT is an efficient signal processing approach for analysis of spectrum of the signals. It effectively provides time-frequency-energy of time series data of current signals. It effectively computes frequency components and amplitudes of transients appearing for short time. Hence, it can be utilized for identification of fault events incident on the transmission line. Processing of current signal (i(t )) using HT is detailed below [17].
Here, PV : Cauchy's principal value integral, t : time, : time period. Proposed Hilbert index (H-index) is computed by taking absolute values of the H (i(t )) using the following command:- H-index has advantages that it gives high magnitude at moment of fault incidence and least affected by noise. Further, it provides physical instantaneous frequencies of transients associated to current signal which improves performance of algorithm to identify the faulty transients. It helps to increase the  Hilbert transform of a current signal shifts the phase angle of all frequency components associated to signal by ±90 • and spectrum of the signal and Hilbert transform of the signal will remain same. Hence, due to this orthogonal property of the Hilbert transform the H-index is observed to increase before occurrence of fault. However, the property of HT to retain the high magnitude for the faulty phase has been combined with the Stockwell transform and Alienation coefficient to design the proposed fault index for identification of faulty event. Orthogonal property of HT will not introduce any delay in identification of faulty event because this demerit has been obviated by the use of Stockwell transform and Alienation Coefficient. Hence, use of the HT to design the proposed protection algorithm improves performance of the protection scheme.

S-index
Signals of currents are recorded on bus-1 of test transmission line and decomposed using Stockwell transform (ST) to compute S-index. The ST effectively extracts information contained in the spectrum of phase and amplitude of current signals. Output of ST based decomposition of current signal is a complex valued matrix (STMC). Each row and column of this matrix gives frequency and time. ST effectively gives high time resolution for the high frequency signals and low time resolution when frequency of signal is small [18]. To realize ST based processing, current signal (i(t )) is processed by application of short time Fourier transform (STFT) computed as detailed below [19].
Here, t : spectral localization time, f : Fourier frequency, : time period, g(t ): Gaussian window function. Stockwell transform is obtained by using following Gausian window function in the equation (3) for processing the current signal i(t ) [20].
Hence, complex valued output matrix (STMC) of the Stockwell transform is computed by the use of following relation [21].
Median of STMC is computed and designated as MS. Further, absolute magnitudes of every column of STMC is computed and designated as SS. Co-variance of SS is computed and assigned the name co-variance factor (COVF). S-index is computed by multiplying the MS, SS and COVF element by element.

A-index
Alienation index (A-index) is computed from the correlation coefficient (CC) using the following relation.
Following relation is used to compute the correlation coefficient (CC) between two current variables i 1 and i 2 located at quarter cycle time difference.
Here, Ns: sample numbers in a cycle (Ns=64 considering sampling frequency of 3.84kHz), i 1 : samples of current at time t 0 , i 2 : samples of current at time −T + t 0 , T: time period of current cycle.

Fault index
Fault index (FI) is computed by computing element to element multiplication of H-index, S-index and A-index using the following relation.
A threshold value of 20,000 is selected for the FI to find the faulty and healthy phases. If FI corresponding to a phase exceeds the threshold magnitude then phase is faulty in nature else phase is healthy. Threshold magnitude of 20,000 is considered for FI to differentiate the faulty and healthy phases by testing the algorithm on 100 data-sets of every fault. Hence, total 500 sets of data have been considered for the PG, PP, PPG, TPF and TPG faults. This data set is computed by variations in the fault parameters such as fault impedance, fault incidence angle (FIA), noise levels, fault location on transmission line, hybrid combination of underground cable and overhead transmission line, flow of power on transmission line in forward and reverse direction etc. It is established that the threshold value of 20,000 is effective to identify the faulty events for all the possible fault scenario which may take place on the transmission line.

Ground fault index
A ground fault index (GFI) is proposed to identify the involvement of ground during the scenario of two phase faults. Since, three phase faults with and without involving the ground are most severe faults and behave in similar manner. Hence, there is no need to identify the ground involvement in these types of faults. GFI is to be computed using the following procedure.
• Compute zero sequence current (ZSC) from the currents of all the three phases using the following relation.
• Decompose ZSC using the Stockwell transform described in section 3.1.2 and compute output complex matrix and designate it as ZSTMC. • Compute absolute values output matrix (ZSTM) from the matrix ZSTMC using the following relation.
• Compute median of ZSTM matrix (ZM) using the following relation:- • Compute summation of every column of ZSTM matrix (ZS) using the following relation:- • Compute co-variance of ZS using the following relation and designate it as zero sequence covariance factor (ZCOVF):- • GFI is computed by multiplying the ZM, ZS and ZCOVF as detailed below:- A ground threshold (GTH) value of 50 is chosen for the GFI to differentiate the PP and PPG faults. This value of GTH decided by testing the algorithm on 100 sets of data considered for the PP, and PPG faults. This data set is computed by variations in the fault parameters such as fault impedance, fault incidence angle (FIA), noise levels, fault location on transmission line, hybrid combination of underground cable and overhead transmission line, flow of power on transmission line in forward and reverse direction etc. Further, the value of GFI greater than GTH indicates the involvement of ground in the fault.

Transmission line faults location estimation
Faults have been located on the power transmission line by the use of simple mathematical power relation described in the following subsections.

PG fault
A curve fitting tool is used to design a mathematical relation for location of PGF on the power line. Following relation is effective to estimate PGF location on transmission line:- where l = length of line from sending end (bus-1) in km; A= constant which is considered equal to 6003; b = −0.3752; C = constant which is considered equal to −6.064; x = mean value of FI computed using FIs associated to all phases as detailed below.

PP fault
Mathematical relation described by the expression (16) also effectively localizes the PPF event on the transmission line. However, variables are described as l = location of PPF from sending end (bus-1) in km; A= constant which is considered equal to −104.7; b = 0.09523; C = constant which is considered equal to 473.5; x= mean value of FI computed using FIs associated to all phases using expression (17).

PPG fault
Mathematical relation described by the expression (16) also effectively localizes the PPF event on the transmission line. However, variables are described as l = length of line from sending end (bus-1) in km; A= constant which is considered equal to 1338; b = −0.04778; C = constant which is considered equal to −603.2; x = mean value of FI computed using FIs associated to all phases using expression (17).

TPG fault
Mathematical relation described by the expression (16) also effectively localizes the TPGF event on the transmission line. However, variables are described as l = length of line from sending end (bus-1) in km; A = constant which is considered equal to 1533; b = −0.03564; C = constant which is considered equal to −830.4; x = mean value of FI computed using FIs associated to all phases using expression (17).

TRANSMISSION LINE FAULT DETECTION AND CLASSIFICATION
This section describes results of simulation to implement suggested approach, to detect and classify fault events incident on power transmission line to design effective protection scheme. Fault scenarios such as PGF, PPF, fault between two phases and involving ground (PPGF), fault on all the three phases

Phase to ground fault
A PGF event is realized on phase-A at center of the test transmission line at 6 th cycle and current signals of all phases are captured on sending end (Bus-1). These signals of current are processed by application of the proposed algorithm to compute H-index, S-index, A-index and FI. Current signal waveform, H-index plot, S-index plot, A-index plot, proposed fault index plot and high resolution FI plot are described in Figure 3(a)-(f), respectively. Figure 3(a) details that current associated to faulty phase-A increased just after fault incidence whereas currents pertaining to phases-B & C retain their original magnitude. H-index associated to faulty phase-A increases just after fault incidence as illustrated in Figure 3(b) indicating the fault event. It is also observed that magnitude of H-index associated to phases-B and C retain the magnitudes same as that observed in the healthy scenario. Sindex associated to faulty phase-A increases just after fault incidence as illustrated in Figure 3(c) indicating fault event. However, magnitude of S-index associated to phases-B & C retain the magnitudes same as that observed in the healthy scenario indicating healthy nature of these phases. A-index associated to faulty phase-A increases just after fault incidence as illustrated in Figure 3 Table 2. Hence, PGF event has been identified effectively by the application of algorithm proposed in this paper. High resolution plot of FI shown in Figure 3(f), helps to estimate the time of fault identification. Time taken by the FI to cross the threshold value is the time of fault estimation. It is inferred that FI first time crosses the pre-set threshold magnitude in time interval of 0.005s and trip command for the circuit breaker will be generated in this time interval.
A PGF event is realized on phase-A at center of the test transmission line at 6 th cycle and current signals of all phases are captured on sending end (Bus-1). The 3 rd , 5 th , and 7 th harmonic components are superimposed on the current signals of all phases. These current signals with harmonic components are processed by application of the proposed algorithm to compute H-index, S-index, A-index and FI. Current signal waveform with harmonic components, H-index plot, S-index plot, A-index plot, proposed fault index plot and high resolution FI plot are described in Figure 4(a)-(f), respectively. Figure 4(a) details that current associated to faulty phase-A has increased just after fault incidence whereas currents pertaining to phases-B and C retain their original magnitude. H-index associated to faulty phase-A increases just after fault incidence as illustrated in Figure 4(b) indicating the fault event. It is also observed that magnitude of H-index associated to phases-B and C retain the magnitudes same as that observed in the healthy scenario. S-index associated to faulty phase-A increases just after fault incidence as illustrated in Figure 4(c) indicating fault event. However, magnitude of S-index associated to phases-B and C retain the magnitudes same as that observed in the healthy scenario indicating healthy nature of these phases. A-index associated to faulty phase-A increases just after fault incidence as illustrated in Figure 4(d) indicating fault event whereas magnitude of A-index associated to phases-B and C retain low magnitudes indicating healthy nature of these phases. FI associated to faulty phase-A increases just after fault incidence as illustrated in Figure 4(e) and becomes higher in comparison to threshold magnitude of 20,000 indicating fault event. Further, FI magnitudes associated to phases-B and C are lower in comparison to threshold magnitude indicating healthy nature of these phases. Hence, PGF event has been identified effectively in the presence of 3 rd , 5 th , and 7 th harmonic components. High resolution plot of FI shown in Figure 4 Figure 5 details that FI associated to faulty phase-A increases just after fault incidence and becomes higher in comparison to threshold magnitude of 20,000 considering the system frequencies of 58 Hz, 59 Hz, 61 Hz and 62 Hz. This indicates that phase-A is faulty in nature. Further, FI magnitudes associated to phases-B and C are lower in comparison to threshold magnitude indicating healthy nature of these phases. Hence, PGF event has been identified effectively considering off-nominal frequencies of 58 Hz, 59 Hz, 61 Hz and 62 Hz. for PPF event are illustrated in Figure 6(a)-(f) in respective sequence. Figure 6(a) details that currents associated to faulty phases-A and B increased just after fault incidence whereas current pertaining to phases-C retains its original magnitude. H-index associated to faulty phases-A and B increase just after fault incidence as illustrated in Figure 6(b) indicating the fault event. It is also observed that magnitude of H-index associated to phase-C retains the magnitudes same as that observed in the healthy scenario. S-index magnitude associated to faulty phases-A and B increase just after fault incidence as detailed in Figure 6(c) indicating the fault event whereas magnitude of S-index associated to phase-C retains the magnitude same as that observed in the healthy scenario indicating healthy nature of this phase. A-index associated to faulty phases-A and B increase just after fault incidence as illustrated in Figure 6(d) indicating fault event whereas magnitude of A-index associated to phase-C retains low magnitudes indicating healthy nature of this phase. FI magnitude associated to faulty phases-A and B increases just after fault incidence as illustrated in Figure 6(e) and becomes higher in comparison to pre-set threshold magnitude of 20,000 which indicates the fault event. Further, FI magnitude associated to phase-C is lower compared to the threshold magnitude indicating healthy nature of this phase. Peak magnitudes of all phases are tabulated in Table 2. Hence, PPF event has been identified effectively by the application of algorithm proposed in this paper. High resolution plot of FI shown in Figure 6 Figure 7(a) details that currents associated to faulty phases-A and B increased just after fault incidence whereas current pertaining to phases-C retains its original magnitude. H-index associated to faulty phases-A and B increase just after fault incidence as described in Figure 7(b) indicating the fault event. It is also inferred that magnitude of H-index associated to phase-C retains the values same as that observed in the healthy scenario. S-index magnitude associated to faulty phases-A and B increase just after fault incidence as illustrated in Figure 7(c) indicating the fault event whereas magnitude of S-index associated to phase-C retains the magnitude same as that observed in the healthy scenario indicating healthy nature of this phase. Aindex associated to faulty phases-A and B increase just after fault incidence as illustrated in Figure 7(d) indicating a fault event whereas magnitude of A-index associated to phase-C retains low magnitudes indicating healthy nature of this phase. FI magnitude associated to faulty phases-A and B increase just after fault incidence as illustrated in Figure 7(e) and become higher in comparison to threshold magnitude of 20,000 which indicates fault event. Further, FI magnitude associated to phase-C is lower in comparison to threshold magnitude which indicates healthy nature of this phase. Peak magnitudes of all phases are tabulated in Table 2. Hence, PPGF event has been identified effectively by application of algorithm proposed in this paper. High resolution plot of FI shown in Figure 7 Hence, behaviour of PPGF event is observed to be similar compared to event of PPF. However, peak magnitudes of FI for the phases slightly differ for the PPF and PPGF events.

Three phase fault
A TPF event is simulated on all the phases at center of test power transmission line at 6 th cycle and current signals of all the phases are captured on sending end (Bus-1). These signals of current are processed using the algorithm to compute H-index, S-index, A-index and FI. Current signal waveform, H-index plot, S-index plot, A-index plot, proposed fault index plot and high resolution FI plot for PPF event are illustrated in Figure 8(a)-(f) in the respective sequence. Figure 8(a) details that currents associated to all the phases are increased just after fault incidence. H-index associated to all phases increases just after fault incidence as described in Figure 8(b) indicating fault event. S-index magnitude associated to all the phases increase just after fault incidence as detailed in Figure 8(c) indicating the fault event. A-index associated to faulty phases increase just after fault incidence as illustrated in Figure 8(d) indicating fault event. FI magnitude associated to all phases increase just after fault incidence as illustrated in Figure 8(e) and become higher compared to the threshold magnitude of 20,000 indicating the fault event. Peak magnitudes of all phases are tabulated in Table 2. Hence, TPF event has been identified effectively by application of algorithm proposed in this paper. High resolution plot of FI shown in Figure 8(f), helps to estimate the time of fault identification. Time taken by the FI for phases-A, B and C to cross the threshold value is the time of fault estimation. It is seen that FI for phases-A, B and C first time crosses the threshold magnitude in time interval of 0.0001 s, 0.0002 s and 0.0003 s, respectively, and trip command for the circuit breaker will be generated in this time interval. Hence, behaviour of TPF event is effectively identified by the use of proposed approach.

Three phase to ground fault
A TPGF event is realized on all the phases and ground at center of the test transmission line at 6 th cycle and current signals of  Figure 9(a)-(f) in respective order. Figure 9(a) details that currents associated to all the phases are increased just after fault incidence. H-index associated to all the phases increase just after fault incidence as detailed in Figure 9(b) indicating fault event. S-index magnitude associated to all phases increase just after fault incidence as described in Figure 9(c) indicating the fault event. A-index associated to faulty phases increase just after fault incidence as illustrated in Figure 9(d) indicating fault event. FI magnitude associated to all phases increase just after fault incidence as illustrated in Figure 9(e) and become higher compared to the threshold magnitude of 20,000 indicating fault event. Peak magnitudes of all phases are tabulated in Table 2. Hence, TPGF event has been identified effectively by application of algorithm proposed in this paper. High resolution plot of FI shown in Figure 9(f), helps to estimate the time of fault identification. Time taken by the FI for phases-A, B and C to cross the threshold value is the time of fault estimation. It is seen that FI for phases-A, B and C first time crosses the threshold magnitude in time interval of 0.0001 s, 0.0002 s and 0.0003 s, respectively, and trip command for the circuit breaker will be generated in this time interval. Hence, behaviour of TPGF event is effectively identified using the proposed approach. Further, behaviour of TPGF event is observed similar as compared to the event of TPF.

Fault classification
Faults are categorized by use of number of phases which are faulty in nature. For event of PGF, number of faulty phase is only one. PPF and PPGF fault events have two faulty phases. Further, TPF and TPGF events have three numbers of faulty phases. Involvement of ground during the events of phase to phase faults can be identified by the use of ground fault index (GFI). GFI computed for the PPF and PPGF is detailed in Figure 10. It is seen that peak magnitude of GFI for event of PGF has crossed the ground fault threshold value of 50 which indicates that ground is involved during fault scenario. Further, peak magnitude of GFI is less than ground fault threshold of 50 Hence, all fault types have been classified effectively. Behavior of TPF and TPGF are same and further differentiation is not required. However, proposed GFI is also effective to differentiate TPF and TPGF from each other.

CASE STUDIES
This section includes the results to test performance of the algorithm for different fault scenarios.

Effect of variation in fault incidence angle
A PGF event is realized on phase-A at center of the test transmission line at 6 th cycle considering fault incidence angles  Figure 12. Further, peak magnitude of FI for all the FIAs is tabulated in Table 3. Figure 11 illustrates that magnitude of current associated to faulty phase-A increases due to incidence of PGF event whereas the magnitude of current associated to healthy phases-B and C are following the sinusoidal nature even after incidence of PGF event. However, due to variations in FIA the change in current of phase-A takes place at different phase angles of current waveform. Figure 12 illustrates that FI associated to phase-A has crossed the threshold value of 20,000 whereas the FIs corresponding to the phases-B & C are lower in comparison

Effect of variation in fault impedance
A PGF event is realized on phase-A at center of the test transmission line at 6 th cycle considering fault impedance equal to 0.01Ω, 1Ω, 2Ω, 5Ω, 10Ω, 20Ω and 30Ω. Current signals of all phases are captured on sending end (Bus-1) and processed by use of algorithm to compute fault index. The values of FI for all the considered fault impedance are tabulated in Table 4. Current signals associated to phase-A during PGF event with variations in fault impedance for 1Ω, 2Ω, 5Ω, 10Ω, 20Ω and 30Ω are illustrated in Figure 13.   Table 4 illustrates that FI associated to phase-A has crossed the threshold value of 20,000 for the fault impedance equal to 0.01Ω, 1Ω, 2Ω, 5Ω, 10Ω, 20Ω and 30Ω. Further, FIs corresponding to the phases-B and C are lower compared to threshold magnitude for all the considered magnitudes of fault impedance. Hence, it is ascertained that phase-A is faulty in nature and phases-B and C are healthy. Hence, algorithm effectively identified PGF event for all possible magnitudes of fault impedance. Further, it is observed from the Figure 13 that magnitude of current associated to faulty phase-A decreases due to increase in the values of fault impedance.

Effect of reverse power flow
The condition of reverse power flow on transmission line is simulated by transferring power from Bus-2 to Bus-1. A PGF event is realized on phase-A at center of the test transmission line at 6 th cycle and current signals of all phases are captured on sending end (Bus-1). These signals of current are processed by use of algorithm to compute H-index, S-index, A-index and FI. Current signal waveform, H-index plot, S-index plot, A-index plot, and proposed fault index plot are illustrated in Figure 14(a)-(e) in respective order. Figure 14(a) details that current associated to faulty phase-A increased just after fault incidence whereas currents pertaining to phases-B & C retain their original magnitude. H-index associated to faulty phase-A increase just after fault incidence as illustrated in Figure 14(b) indicating fault event. It is also observed that magnitude of H-index associated to phases-B and C retain the magnitudes same as that observed in the healthy scenario. S-index associated to faulty phase-A increases just after fault incidence as illustrated in Figure 14(c) indicating fault event whereas magnitude of S-index associated to phases-B and C retain the magnitudes same as that observed in the healthy scenario indicating healthy nature of these phases. A-index associated to faulty phase-A increases just after fault incidence as illustrated in Figure 14(d) indicating fault event whereas magnitude of A-index associated to phases-B and C retain low magnitudes indicating healthy nature of these phases. FI associated to faulty phase-A increases just after fault incidence as illustrated in Figure 14(e) and becomes higher compared to the threshold magnitude of 20,000 indicating fault event. Hence, PGF event has been identified effectively by the application of proposed algorithm during the scenario of reverse flow of power on the transmission line. Hence, proposed algorithm effectively identified the PGF event for the scenario of reverse flow of power on the transmission line.

Effect of line loading
Performance of algorithm is established for investigation of PGF event considering line loading realized by connecting a load comprising of 50 MW and 10 MVA (inductive) on bus-2 of transmission line. A PGF event is realized on phase-A at center of the transmission line at 6 th cycle. Current signals of all the phases are captured on sending end (Bus-1) and processed by the use of algorithm to compute fault index. Current waveform and FI are illustrated in Figure 15(a) and (b) in respective order. Figure 15(a) details that current associated to faulty phase-A has increased just after fault incidence whereas currents pertaining to phases-B and C retain their original magnitude. FI associated to faulty phase-A increases just after fault incidence as illustrated in Figure 15(b) and becomes higher compared to the threshold magnitude of 20,000 indicating fault event. Hence, PGF event has been identified effectively by the application of proposed algorithm during the scenario of loading on the transmission line. Hence, proposed algorithm effectively identified the PGF event during the scenario of loading on the power transmission line.

Effect of noise
Performance of algorithm is established in noisy scenario with noise level of 10 dB SNR. A PGF event is realized on phase-A at center of the power transmission line at 6 th cycle and current signals of all phases are captured on sending end (Bus-1). Gaussian noise having level 10 dB SNR is superimposed on these  Figure 16(a)-(e) in respective sequence. Figure 16(a) details that current associated to faulty phase-A increased just after fault incidence whereas currents pertaining to phases-B and C retain their original magnitude. Hindex associated to faulty phase-A increase just after fault incidence as illustrated in Figure 16(b) indicating fault event. It is also observed that magnitude of H-index associated to phases-B and C retain the magnitudes same as that observed in the healthy scenario. It is inferred that performance of H-index is not affected by the presence of noise. S-index associated to faulty phase-A increases just after fault incidence as illustrated in Figure 16(c) indicating fault event whereas magnitude of Sindex associated to phases-B and C retain the magnitudes same as that observed in the healthy scenario indicating healthy nature of these phases. It is inferred that performance of S-index is slightly affected by the presence of noise. A-index associated to faulty phase-A increases just after fault incidence as illustrated in Figure 16(d) indicating fault event whereas magnitude of A-index associated to phases-B and C retain low magnitudes indicating healthy nature of these phases. It is inferred that performance of A-index is greatly affected by the presence of noise. Sharp ended peaks are generated due to presence of noise. FI associated to faulty phase-A increase just after fault incidence  Figure 17(a) details that current associated to faulty phase-A increased just after fault incidence and again regains the original value after fault clearance. Small magnitude transients persist after fault clearance and finally dies out in 3 to 5 cycles. Magnitude of currents pertaining to phases-B and C retain their original magnitude. FI associated to faulty phase-A increase just after fault incidence as illustrated in Figure 17 At the time of fault clearance at 8 th cycle the peak magnitude of FI for phase-A is lower compared to the threshold magnitude which indicates that the circuit breaker will remain closed. It is also observed that the FI associated to the phases B and C is lower compared to the threshold value indicating the healthy nature of these phases. Further, generally the fault clearance takes place when line is opened by the auto-recloser and current waveform will be discontinued. Hence, FI at the time of fault clearing will be zero.

DIFFERENTIATING OPERATIONAL EVENTS FROM THE FAULT EVENTS
This section details the results to test performance of algorithm for switching transients.  Figure 18(a)-(f) in respective order. Figure 18(a) details that current associated to all phases slightly increases in the period between 4 th cycle and 8 th cycle. H-index associated to all phases slightly increases in the period between 4 th cycle and 8 th cycle as illustrated in Figure 18(b) indicating that event is not faulty. S-index associated to all phases has sharp magnitude peaks at the time of 4 th cycle and 8 th cycle when switching event occurs as depicted from Figure 18(c). Aindex associated to all phases has increased at 4 th cycle and 8 th cycle when switching event occurs as depicted from Figure 18(d). FI associated to all phases increases at 4 th cycle and 8 th cycle when switching event occurs as depicted from Figure 18(e) and (f). Peak magnitude of FI is lower in comparison to threshold magnitude of 20,000. Hence, this event will not be categorized as faulty event and subsequently no tripping command will be generated for circuit breaker. Hence, proposed algorithm is effective to discriminate the switching events from the faulty events.  Figure 19(a)-(f) in respective order. Figure 19(a) details that current associated to all phases slightly decreased in the period between 4 th cycle and 8 th cycle. H-index associated to all phases slightly decreased in the period between 4 th cycle and 8 th cycle as illustrated in Figure 19(b) indicating that event is not faulty in nature. Small magnitude transients are also observed at the instant of switching on the capacitor. S-index associated to all phases has sharp magnitude peaks at the time of 4 th cycle and 8 th cycle when switching event occurs as depicted from Figure 19(c). A-index associated to all phases has increased at 4 th cycle and 8 th cycle when switching event of capacitor occurs as depicted from Figure 19(d). FI associated to all phases increases at 4 th cycle and 8 th cycle when switching event occurs as depicted from Figure 19(e) and (f).

Load switching
High resolution figure of FI index described in Figure 19(f) indicates the variations of FI at moments of switching the capacitor. It is inferred that FI is lower compared to threshold magnitude of 20,000. Hence, this event will not be categorized as faulty event and subsequently no tripping command will be generated for circuit breaker. Hence, proposed algorithm is effective to discriminate the switching events from the faulty event.

ESTIMATION OF FAULT LOCATION ON TRANSMISSION LINE
Faults have been located on the power transmission line by use of the mathematical relations described in the Section 3.2. FI is computed for all the phases during faulty events. Average value of the FI (FIM) for all phases is considered for fault locations. FIM computed during the scenario of PGF, PPF, PPGF and TPGF are included in Table 5.
Location of faulty event on the transmission line is estimated using the relation (16) described in Section 3.2.1 considering FIM values for the variable x tabulated in Table 5. Locations of faulty events have been estimated using the proposed algorithm for actual transmission line lengths of 10 km, 40 km, 70 km, 100 km, 130 km, 160 km, 190 km, and 220 km. Estimated line lengths and error between the actual line length and estimated line length have been provided in Table 6. Error between the estimated location using the proposed method and actual location of fault on power transmission line is computed using the following relation.  Table 6. It is seen that maximum error between the ELL and ALL is less than 3% and mean error is less than 1%. Further, it is observed that error is maximum for the locations situated near the sending bus of the line. It is greater than 2% for the fault locations of 10 km and 40 km. Error falls between 1% and 2% for the transmission line length of 100 km. For, all other locations the error is less than 1%. Therefore, it is estab- lished that for most of the locations of the fault event on the transmission line the error is less than 1%. Hence, proposed method effectively localizes the faulty events on the transmission line with high accuracy and minimum error between the actual line length and estimated line length.

TESTING OF ALGORITHM ON REAL TIME TRANSMISSION NETWORK
Performance of the proposed protection algorithm is tested on the real time transmission grid of Rajasthan state of India. This transmission network is a practical complex integrated network operated on voltage levels of 765 kV, 400kV, 220 kV, and 132 kV. Various types of generating plants such as nuclear power plant (NPP), coal and gas based thermal power plants (TPS), wind power plant (WPP), solar power plant (SPP) and biomass power plant are injecting power to this network. At consumer ends, this network is transferring power to the distribution network operated at voltage levels of 33 kV, 11 kV and 0.44 kV. Details of transformers installed on the various grid sub-stations (GSS) of this transmission network is provided in Table 7. Total circuit length of transmission lines of the transmission network  in Rajasthan is included in Table 8. Source wise generation capacity of power plants integrated to the transmission network of Rajasthan is provided in Table 9 [22]. Performance of the algorithm is validated on a transmission line operating on the voltage level of 400 kV between the 400 kV GSS Merta and 400 kV GSS Kota. This is a single circuit line of 256 km and uses twin moose conductor of 515 MW surge impedance loading (SIL). Data of a PG fault incident at a distance of 123.47 km is taken from the disturbance recorder installed at the 400 kV GSS Merta and analyzed using the proposed algorithm to compute the fault index which is illustrated in Figure 20. It is observed that peak magnitude of the fault index is higher compared to the threshold. Hence, a PG fault event incident on a practical transmission line has been identified effectively by the use of proposed algorithm. Further, the fault location is also estimated using the pro- posed algorithm which is found equal to 125.92 km. Therefore, the fault location has been estimated with an error of 1.984%. Hence, proposed algorithm has effectively identified and located the PG fault event on a transmission line of a practical complex nature transmission network operated at different voltage levels where different types of the generators are integrated.

PERFORMANCE COMPARATIVE ANALYSIS
Performance of the proposed algorithm is evaluated and compared with algorithms using alienation coefficient [23], time frequency approach [24], and discrete Fourier transform [4]. Performance comparative study with respect to various parameters is included in Table 10 using eleven parameters. These parameters include maximum error, mean error, sampling frequency, fault estimation time, estimation of fault location, classification of fault, effect of noise on performance of algorithm, effect of line loading, effect of fault impedance, FIA variation, and reverse power flow. Effectiveness of an algorithm for a specific scenario/condition is indicated by Investigated and Not investigated to indicate that algorithm either not tested or fails for particular criteria. It is inferred from Table 10 that proposed method is more effective compared to the methods reported in [23], [24], and [4] in terms of investigated eleven different parameters. Further, mean error is reduced significantly by application of proposed algorithm. Scope of proposed algorithm is wide compared to the methods reported in [23], [24] and [4].

CONCLUSION
A current signal supported hybrid algorithm using ST, HT and ACF is presented in this paper which is effective for identification and classification of faults incident on power transmission line. Faults are effectively classified by estimation of number of faulty phases and a ground fault index (GFI). Faults have been effectively located on power transmission line by the use of a simple mathematical formulation. It is concluded that proposed approach is effective to detect and classify faults such as PGF, PPF, PPGF and TPGF incident on transmission line. Algorithm is effective to recognize the faulty scenario with variations in fault impedance, FIA, reverse power flow, effect of line loading, transient faults, off-nominal frequency and presence of harmonic components. Algorithm effectively recognizes the faults in noisy scenario with high noise level of 10dB SNR. Proposed algorithm effectively located the fault conditions on transmission line with a mean error less than 1%. Proposed protection algorithm effectively identified the fault event incident on a 400 kV transmission line of a real time grid. Performance of algorithm is superior compared to approaches based on Alienation coefficient, time frequency analysis and DFT which have been reported in literature.