Wavelet packet transform applied to a series-compensated line: A novel scheme for fault identification

Journal Pre-proofs Wavelet Packet Transform Applied to a Series-Compensated Line: A Novel Scheme for Fault Identification Ahmed R. Adly, Shady H.E. Abdel Aleem, Mahmoud A. Elsadd, Ziad M. Ali PII: DOI: Reference:

S0263-2241(19)31022-X https://doi.org/10.1016/j.measurement.2019.107156 MEASUR 107156

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Measurement

Received Date: Revised Date: Accepted Date:

5 July 2019 6 October 2019 12 October 2019

Please cite this article as: A.R. Adly, S.H.E. Abdel Aleem, M.A. Elsadd, Z.M. Ali, Wavelet Packet Transform Applied to a Series-Compensated Line: A Novel Scheme for Fault Identification, Measurement (2019), doi: https:// doi.org/10.1016/j.measurement.2019.107156

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© 2019 Published by Elsevier Ltd.

Wavelet Packet Transform Applied to a SeriesCompensated Line: A Novel Scheme for Fault Identification Ahmed R. Adlya*, Shady H. E. Abdel Aleemb, Mahmoud A. Elsaddc, and Ziad M. Alid,e aNuclear

Research Center, Atomic Energy Authority, Egypt ([email protected]) of May Higher Institute of Engineering, Mathematical and Physical Sciences Department, Helwan, Cairo, Egypt ([email protected]) cFaculty of Engineering, Menoufia University, Egypt ([email protected]) dElectrical Engineering Department, College of Engineering at Wadi Addawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia eElectrical Engineering Department, Aswan faculty of Engineering, 81542, Aswan University, Egypt ([email protected]) b15th

*Corresponding

author: T: +201229318283 | E-mail address: [email protected]

Abstract—For series-compensated transmission lines (SCTLs), identification of the fault section with respect to the compensator as well as fault phase selection are important issues. In this paper, first, the various methods applied for SCTLs are classified and discussed according to specified performance indices selected by the operator. Further, an investigation of solutions to their drawbacks is presented. Second, a novel scheme based on the application of wavelet packet transform (WPT) is proposed for an SCTL. A db10 wavelet packet is used for decomposing the faulted phase current waveform to obtain the energy coefficients. Third, the ATP/EMTP package is used to test and validate the proposed scheme, in which several fault scenarios with different fault locations, inception angles, fault resistances, noise, and variation in voltage and source impedance are examined to show its robustness. The effectiveness of the proposed scheme is demonstrated compared to other methods in the literature. Keywords—Fault classification; fault detection and section identification; series compensation; transmission lines; wavelet packet transform.

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1.

Introduction

Connecting series capacitors into transmission lines has several benefits such as improving the transmittable power, reducing the transmission losses and voltage drop, increasing the system stability and enhancing the voltages profile. However, it can lead to some problems in the relay functionality due to the nonlinear behavior of the series capacitor arrangement [1]. From a stability point of view, fault detection (FD), fault classification (FC) and fault section identification (FSI) are the main issues for both transmission and distribution power systems. For example, to estimate the fault distance in an SCTL, a distance relay requires a fault section identifier for the discrimination of faults to be encountered or not [2]. In the literature, several schemes have been reported for FD, FC, and FSI in SCTLs [3–10]. FD and FC aim to determine the fault phase selection. FSI aims to determine the fault location and to show whether the fault is before or after the series capacitor from the relay point perspective. In these schemes, the most important issue is how to extract the transients’ features from the original fault signal. In this regard, wavelet transform (WT) has been selected as an effective tool for analyzing the fault transients because of its good time-frequency localization ability [11–13]. In [14], the performance of Fourier transform (FT) and WT was evaluated in classifying and locating various faults applied to high voltage transmission lines (HVTL) and it was clearly noted that better results for FC were provided by the WT technique. In this work, different techniques for FD, FC and FSI in SCTLs are discussed, and an investigation of solutions to their drawbacks is presented. Further, a proposed adaptive discrimination scheme derived in the spectral domain and based on the application of wavelet packet transform (WPT) is proposed for SCTLs. The proposed scheme is a single-end approach. It depends only on the available information at the sending end of the power TL. Moreover, it does not use a threshold level, so no adjustment will be needed for different transmission systems. Third, the ATP/EMTP package is used to test and validate the proposed scheme in which several fault scenarios with different fault locations, inception angles and fault resistances are examined to show its robustness. The effectiveness of the proposed scheme is demonstrated compared to other methods in the literature. This paper is organized as follows: Section 2 describes the recent techniques for FSI in SCTLs. Section 3 presents the WT challenges in the detection and classification of faults. Section 4 presents the main features of the proposed scheme. Section 5 presents the system under study, simulation and results for various fault types, locations, inception angles and fault resistance. In Section 6, generalization of the scheme proposed is presented and discussed. Section 7 presents a comparison between the proposed scheme and other schemes reported in the literature. Section 8 is dedicated to the conclusions and future works. -2-

Nomenclature C0 C1 FZ Ia, Ib, and Ic Ig Im N P q Sf Sth VREF Z0 Z0SA Z0SB Z1 Z1SA Z1SB

Zero sequence capacitance of line Positive sequence capacitance of line Energy coefficient index of the modal current Three-phase currents in ampere Ground current Modal current Number of coefficients at nodes Reference current for metal-oxide varistors Exponent for metal-oxide varistors Sampling frequency in kHz Threshold value Reference voltage for metal-oxide varistors Zero sequence impedance of line Zero sequence impedance of system A Zero sequence impedance of system B Positive sequence impedance of line Positive sequence impedance of system A Positive sequence impedance of system B

List of Abbreviations ANFIS ANN ATP/EMTP ChNN CUSUM DT DWPT DWT EBP ELM FC FD FL FSI FT FZI HVTL ICA LST MCSVM MMG MOVs

Adaptive neuro-fuzzy inference system Artificial neural networks Electromagnetic Transients Program Chebyshev neural network Cumulative sum of change in the magnitude Decision trees Discrete wavelet packet transform Discrete wavelet transform State estimation-based protection Extreme learning machine Fault classification Fault detection Fuzzy logic Fault section identification Fourier transform Fault zone identification High voltage transmission line Independent component analysis Least-square technique Multi-class support vector machine Multi-resolution morphological gradient Metal-oxide varistors -3-

PNN RPF RT SCs SCTLs SD SE SNR ST SVM TCSC TL TW WE WPT WT 2.

Probabilistic neural network Reactive power factor Regression tree Series capacitors Series-compensated transmission lines Standard deviation Spectral energy Signal-to-noise ratio S-Transform Support vector machine Thyristor-controlled series compensator Transmission line Traveling wave Wavelet entropy Wavelet packet transform Wavelet transform FD, FC and FSI different techniques: An overview

General categories for FD, FC and FSI schemes in SCTLs are presented in this section as follows: 2.1. FD, FC and FSI schemes based on WT For transmission line fault identification, numerous WT applications such as WPT, discrete wavelet transform (DWT), spectral energy (SE) and wavelet entropy (WE) were investigated. The following literature describes each of these schemes from a critical view point. In [3], a scheme was presented based on WT in conjunction with a regression tree (RT) that detects and classifies the type of fault and locates it in the SCTL. WT provides the hidden information on the fault location, which is the input to the RT. In [4], a scheme was presented based on DWT in conjunction with independent component analysis (ICA) for fault detection. In this scheme the DWT used for analysis the negative sequence fault current signal. In [5], a scheme was presented based on WT only. The three-phase voltages and the SE values are calculated based on different mother wavelets sym7, sym8, db15 and coif5 for different frequency bands. In [6], a scheme was presented based on DWT in conjunction with standard deviation (SD). In this scheme, db4 mother wavelets are applied to the current signals only during fault conditions for one cycle window with a sampling frequency (Sf) of 10 kHz. In [7], a scheme was presented based on DWT. The three-phase and ground currents values are decomposed based on different mother wavelets Haar and db4 for frequency bands in the range of 1–3 kHz. In [8], DWT and WE calculations are used to analyze fault current and voltage signals of the compensated TL. The WE coefficients for currents and voltages are used to detect, classify and identify fault zones based on different fixed threshold values. In [9], FD, FC and zone identification were investigated by using WPT analysis. -4-

The level of lower frequency components is used to detect the fault; the level of higher frequency components is used to decide the FZ. In [10], a scheme was presented based on DWT, which detects and classifies the type of fault and locates it in the SCTLs based on different fixed threshold values. 2.2. Intelligent WT-based classifiers The following section gives an overview of the three categories that combine the WT and intelligent classifiers, namely artificial neural networks (ANN), support vector machine (SVM) and fuzzy logic (FL) for transmission line FD and FC. The authors of [15] and [16] presented a new FZI based on Undecimated DWT and the Chebyshev neural network (ChNN). Undecimated DWT analysis methods were employed to extract data from each simulated faults, and then FZI is accomplished by ChNN. The capability of the proposed scheme was tested for a total of 52,200 test cases. In [17], [18] and [19], a scheme was presented based on DWT and S-transform (ST) combined with a probabilistic neural network (PNN). In [17], the three-phase voltages are decomposed based on DWT to get low and high frequency components with a sampling rate of 50 kHz, and then FZI is accomplished by PNN. In [20], a scheme was presented based on WT and ANN to get an adaptive protection scheme with high accuracy. The three-phase currents are decomposed based on DWT with a db4 mother wavelet to get low and high frequency components with a sampling rate of 20 kHz, and then FZI is accomplished by ANN. In [21], a scheme was presented based on discrete WPT, ChNN and SVM. The half-cycle post fault current signals are used with a 4 kHz sampling rate through DWPT. A second level of decomposition has been found to be necessary and sufficient for proper FC. In [22], a scheme was presented based on WT and an adaptive neuro-fuzzy inference system (ANFIS). The ANFIS architecture consists of ANN and FL algorithms. The three-phase currents and voltages are decomposed based on WT with a db4 mother wavelet with a sampling rate of 8 kHz, and then FZI is accomplished by ANFIS. The authors of [23] presented a scheme based on DWT and SVM. The proposed scheme uses the samples of three-phase currents for one cycle duration. Initially, the line currents are extracted by first-level decomposition of the current samples using a db2 mother wavelet with a sampling rate of 4 kHz. Then, the extracted features are used as inputs to an SVM for determining the FZ. In [24] and [25], a scheme based on WT and an extreme learning machine (ELM) was presented. The features of fault currents are extracted by first-level decomposition of the current signal using DWT (db2 and db8 mother wavelet, respectively) with sampling rates of 1.6 kHz and 1.25 kHz respectively, and the extracted features are applied as inputs to ELMs. The authors of [26] presented a scheme based on DWT and a multi-class SVM (MCSVM). The features of fault currents are extracted by first-level decomposition of the current signal using DWT

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(db5 mother wavelet) with a sampling rate of 1.6 kHz and the extracted features are applied as inputs to MCSVM. 2.3. FD, FC and FSI schemes based on artificial intelligent classifiers Artificial intelligent classifiers play a main role in the applications related to protective classification [27–32]. In recent years, ANN, SVM, FL, and decision trees (DT) have been widely used in protection schemes. In [27], a scheme was presented based on DT for FC and FZI. One cycle postfault current and voltage samples are used as input vectors for DT with a 1 kHz sampling rate. In [28] and [29], a scheme based on SVM was presented. Ten samples of currents from each phase were selected at Sf of 1.0 kHz as input for the SVM. In [30], also a scheme based on SVM with a Sf of 4 kHz is proposed. In [31] and [32], a scheme was presented based on ANN and ChNN, respectively. The fundamental current and voltage signals are used as input to the intelligent scheme, which detects the fault on the TL and then identifies the section of the fault. In [33], a comparison between two schemes ANN and SVM, was presented, for fault type classification for a TL equipped with a thyristorcontrolled series compensator (TCSC). Both schemes were tested over 19,200 fault cases. It was proved that the SVM scheme is better than the ANN scheme based on the accuracy of the kernel function and other SVM variables. In [34], a scheme based on FL was presented. The DC component from each phase was selected at Sf of 1.0 kHz as input for FL. 2.4. FD, FC and FSI schemes based on voltage and current components This scheme depends on measuring the fundamental and DC components in the phase current of the TL [35], [36] or the superimposed apparent power [37]. In [35], the DC component of the line current at both ends was used to detect the fault zone in SCTLs. In [36], four new schemes were presented for FZI and the authors compared them with each other. Two schemes are based on the direct current component of currents and voltages, and operate using data from both line ends. The third and fourth schemes are based on only one end’s data and use the instantaneous current behavior and instantaneous power waveform behavior, respectively. In [37] and [38], the detection of a fault in a SCTL during a power swing is considered with Sf of 1 kHz. In [37], a technique based on superimposed apparent power is suggested to detect the fault using the least square technique (LST). In [38], a cumulative sum of change in the magnitude (CUSUM) of a negative sequence current to detect faults is used. In [39], a scheme based on the averages of the voltage and current signals was presented. The signal average can be calculated by the sum of all samples of the signal within a full cycle divided by the rate of sampling. During normal conditions, the averages are almost zero, while, following a fault, they change from zero to non-zero values.

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In [40], a scheme based on the estimated reactive power factor (RPF) and differential current with a modified setting was presented. The RPF is measured at both the relay ends with a sampling rate of 1 kHz. In [41], the authors presented a dynamic state estimation-based protection (EBP) scheme to address the challenges of SCTLs. 2.5. FD, FC and FSI schemes based on traveling wave (TW) These schemes utilize high frequency voltage or current signals to detect, classify and identify the fault zone. In [42], a new and fast scheme for fault zone detection based on the high frequency traveling was presented. The scheme practises the relation of magnitude and polarity between wave fronts of high frequency TWs. Then, by comparing the polarity of high frequency TWs extracted by wavelet coefficients, the fault zone is detected. In [43], a scheme based on the pattern of TWs generated during a fault event was presented. DWT is used to investigate the high frequency pattern generated during the fault. In [44], detection of a fault in SCTLs during a power swing is considered with a sampling rate of 10 kHz. The scheme extracts the fault-induced voltage and current components based on the multiresolution morphological gradient (MMG). Then, the fault-initiated forward TW is calculated. Finally, a SVM is used to distinguish faults from other normal capacitor and switching transients. In [45], the authors presented two schemes based on TW and ANN for FD, FC and phase selection for SCTLs. However, these schemes require a large amount of calculation to sum up the final result, making them slow. Also, it was noted that TW is almost absent when the voltage fault inception angle is near to zero. 3.

Fault classification and detection challenges

3.1. Challenges Table 1 summarizes the mean aspects of the different schemes based on FD, FC and FZI for SCTLs. 3.2. Description of proposed scheme: perception towards challenges 3.2.1. Calculation for Decision Making Basically, the WPT is a known tool to analyze the transient phenomena and to extract information (time and frequency) from the transient signal. The advantages behind wavelet analysis and the comparison with Fourier analysis have been reported in [46] and [47]. In this work, a new fault zone detection and identification scheme is proposed. The proposed scheme is able to perform the following functions: FD, FC, and FZI. The proposed methodology for fault zone detection comprises both the high and low frequency harmonic components to enhance the scheme’s performance, while giving a reliable indication of fault zone detection. In addition, it examines the load current continuously, and adaptively changes the threshold value. -7-

Table 1 Comparative study between different schemes Ref.

Algorithm used

Process type

FD & FC

FZI

[3]

DWT, WE

WE for current coefficients

√

√

Not reported

[6]

WT, SD

√

√

10

[7] [8]

DWT DWT, WE

√ √

√ √

200 10

[9]

WPT

√

√

1.6

[10]

DWT

Current coefficients

√

×

[38]

CUSUM

Negative sequence current

√

×

Not reported 1

[40]

NR

Positive sequence voltage and current and RPF

√

√

1

[4]

DWT

ICA and SD for negative sequence current

√

×

Not reported

[15],[16] [20] [25]

√ √ √

√ √ √

4 20 1.25

√

√

4

[17]

DWT, ChNN WT, ANN WT, ELM DWT, ANN, SVM DWT, TW , PNN

√

√

50

[18]

ST, PNN

√

√

1

[19] [23] [26]

WT, PNN DWT, SVM DWT,MCSVM DWPT, ChNN, SVM

√ × √

× √ ×

20 4 1.6

√

×

4

√

√

8

√

√

1.6

√ √ √

√ √ ×

√

×

√ √ √

× × ×

1 1 4 Not reported 4 1 1

√

√

3.2

√

×

80

√

√

400

√

×

100

√

×

10

[33]

High frequency components of current. SE for phase currents WE for current coefficients Fundamental and harmonic component of currents

Detailed coefficients of currents

[22]

WT, ANFIS

[24]

WT, ELM

[27] [28],[29] [30]

DT

Detailed coefficients of voltages Low frequency components of currents Low and high frequency components of currents Approximated and detailed coefficients of currents Approximated and detailed coefficients of currents and voltages High frequency components of currents Fault currents and voltages

SVM

Fault currents

ANN, ChNN

Fundamental component of currents and voltages

[21]

[31] [32] [34] [37]

FL LST

[39]

Average value

[43]

WT, PNN, TW

DC component Superimposed apparent power Superimposed components of voltage and current SE for phase voltages Modulus maxima of wavelet coefficients at high scales Detailed coefficients of voltages

[44]

TW, SVM, MMG

Coefficients of voltages and currents

[5] [42]

WT, TWs

Sf

(kHz)

Observation All schemes use a fixed threshold value having the following limitations.  With a change in power system configuration or when applying any scheme in another system with a different voltage range, a novel threshold should be determined.  The several causes of faults and factors such as source parameters, prefault loading, atmospheric conditions, fault position and line construction that influence the actual waveforms of the secondary arc voltage may hinder the effectiveness of these schemes.  The negative sequence component is suitable for asymmetrical faults, but fails for symmetrical faults.

All these techniques are dependent on huge samples and training for knowledge representation,  Leads to excessively complicated task. Also, they cannot manage the several factors in the transmission system with their uncertainties, which will have an impact on reliability of FD, FC and FZI.  For both FC and the FZI, they need a different feature extraction stage to be applied, leading to a decrease in the overall speed of operation of the scheme and making it difficult to implement.

 Need the pre-fault components data of voltage and current.  Need high Sf.  TW requires specially designed transducers.  Need a large amount of calculation.  Almost, TW is absent when the voltage fault inception angle is near to zero.

The presence of a capacitor in the circuit increases the order of the circuit and changes the voltage waveform and current, particularly the DC and harmonics components waveform. In the presented scheme for fault zone detection (before or after placement of the capacitor), current DC and harmonics components are used. So, the presented scheme employs the amplitude of the modal current DC and -8-

harmonic components as the most appropriate parameter giving a reliable indication of fault zone detection. The three-phase currents Ia, Ib and Ic are combined to form the modal current signal as follows: (1)

𝐼𝑚 = 𝛼𝐼𝑎 ― 𝛽𝐼𝑏 + 𝛾𝐼𝑐

where 𝐼𝑚is the modal current, 𝐼𝑎, 𝐼𝑏 and 𝐼𝑐 denote the measured three-phase currents, α, 𝛽 and γ are the modal signal coefficients, which are considered as 1, –2 and 2, respectively, to relegate the transient behavior of current signals in normal and fault situations. The selected coefficients confirm the preservation of all transients in the three-phase current signals. The selection is based on the modal current signal that cover all fault types encountered in protection. It should be noted that in [48] and [49], two modal signals were used to cover all fault types; however, the simulations presented in this paper show that the modal signal represented in (1) is sufficient for all fault types. Using the modal signal, any common-mode signal (due to mutual coupling between adjacent circuits sharing the same right of way) can be eliminated [48]. This ensures immunity to all disturbances other than those associated with the line to which the protection equipment is connected. Figure 1 shows the flowchart of the suggested scheme. Start n=n+1

Initiate moving window (one cycle) with new sample data Up-data window and read Ia, Ib, and Ic for this window

Calculate Im & Ig (Im=Ia-2Ib+2Ic) & (Ig=Ia+Ib+Ic) Decomposing Ia, Ib, Ic, Im, Ig using WPT Calculate Sa, Sb, Sc, Sg, Da, Db, Dc, Fz

No If ǁ Is-loadǁ >Δ i

Da>0 & Sa>Sth Or (&) Db>0 & Sb>Sth Or (&) Dc>0 & Sc>Sth

Yes Yes Based on Sa, Sb, Sc, Sg, Da, Db, and Dc

Wait 3 cycles

If Fz is null No Yes

Change Sth adaptivley Sth=1.6(Sa+Sb+Sc)/3

Fault detect

Fault classify

Fault after compensation

Fault before compensation

Fig. 1. Flowchart of the proposed scheme. The steps of the fault identification procedure are: 

Sampling the current signal at 6.4 kHz.



Decomposing Ia, Ib, Ic, Im and the ground current Ig. -9-



Decomposing the sampled current signal using a db10 wavelet into level 7 to obtain the proposed nodes’ energy coefficients at different low, high, DC and harmonics frequency ranges as presented in Table 2. Table 2 Proposed energy nodes for different frequency ranges Node Node [1, 0] Node[1, 1] Node [7, 3] Node [7, 4] Node [7, 5]



Frequency range in Hz From to 0 1600 1600 3200 75 100 100 125 125 150

Node Node [7, 6] Node [7, 7] Node [7, 8] Node [7, 9] Node [7, 10]

Frequency range in Hz From to 150 175 175 200 200 225 225 250 250 275

Computing the values for approximating coefficients (maximum absolute values) of current signals (𝑆𝑎 𝑆𝑏 𝑆𝑐,𝑆𝑔) in node [1, 0] and the values for the detailed coefficients (maximum absolute values) of current signals (𝐷𝑎, 𝐷𝑏,𝐷𝑐) in node [1, 1] of the decomposed currents and normalizing it.



Classifying the types of faults and then specifying the proper trip characteristics. It should be noted that the proposed scheme classifies the fault conditions according to the rules reported in Table 3.



Computing the energy coefficient index FZ of the modal current for fault zone detection. Therefore, the energy coefficient index at nodes [7, 0], [7, 3], [7, 4], [7, 5], [7, 6], [7, 7], [7, 8], [7, 9] and [7, 10] which contain DC and harmonics components are computed as: N [7,10] N FZ    d 2K (i )   d 02  i  i 1 K [7,3] i 1

(2)

where dK and N are the coefficients and the number of coefficients at nodes [7, 0], [7, 3], [7, 4], [7, 5], [7, 6], [7, 7], [7, 8], [7, 9] and [7, 10]. 

FZ has been used for fault zone detection. If the index remains null, the fault is after the capacitor. Otherwise, the fault is before the capacitor.



Finally, the healthy condition (no fault) is accomplished with a large difference between the stored load current and the root-mean-square (rms) current value. In addition to that, the detailed coefficients of current signals (𝐷𝑎, 𝐷𝑏, 𝐷𝑐) in node [1, 1] have no value (equal zero), which reflects the change in generating operating conditions.

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Table 3 Fault classification conditions and rules Fault type AG BG CG ABG BCG ACG AB BC AC ABCG

𝑆𝑎 𝐷𝑎 𝑆𝑎 > 𝑆𝑡ℎ 𝐷𝑎 > 0 𝑆𝑎 < 𝑆𝑡ℎ 𝐷𝑎 < = 0 𝑆𝑎 < 𝑆𝑡ℎ 𝐷𝑎 < = 0 𝑆𝑎 > 𝑆𝑡ℎ 𝐷𝑎 > 𝐷𝑡ℎ 𝑆𝑎 < 𝑆𝑡ℎ 𝐷𝑎 < = 0 𝑆𝑎 > 𝑆𝑡ℎ 𝐷𝑎 > 𝐷𝑡ℎ 𝑆𝑎 > 𝑆𝑡ℎ 𝐷𝑎 > 𝐷𝑡ℎ 𝑆𝑎 < 𝑆𝑡ℎ 𝐷𝑎 < = 0 𝑆𝑎 > 𝑆𝑡ℎ 𝐷𝑎 > 𝐷𝑡ℎ 𝑆𝑎 > 𝑆𝑡ℎ 𝐷𝑎 > 𝐷𝑡ℎ

𝑆𝑏 𝐷𝑏 𝑆𝑏 < 𝑆𝑡ℎ 𝐷𝑏 < = 0 𝑆𝑏 > 𝑆𝑡ℎ 𝐷𝑏 > 𝐷𝑡ℎ 𝑆𝑏 < 𝑆𝑡ℎ 𝐷𝑏 < = 0 𝑆𝑏 > 𝑆𝑡ℎ 𝐷𝑏 > 𝐷𝑡ℎ 𝑆𝑏 > 𝑆𝑡ℎ 𝐷𝑏 > 𝐷𝑡ℎ 𝑆𝑏 < 𝑆𝑡ℎ 𝐷𝑏 < = 0 𝑆𝑏 > 𝑆𝑡ℎ 𝐷𝑏 > 𝐷𝑡ℎ 𝑆𝑏 > 𝑆𝑡ℎ 𝐷𝑏 > 𝐷𝑡ℎ 𝑆𝑏 < 𝑆𝑡ℎ 𝐷𝑏 < = 0 𝑆𝑏 > 𝑆𝑡ℎ 𝐷𝑏 > 𝐷𝑡ℎ

𝑆𝑐 𝐷𝑐 𝑆𝑐 < 𝑆𝑡ℎ 𝐷𝑐 < = 0 𝑆𝑐 < 𝑆𝑡ℎ 𝐷𝑐 < = 0 𝑆𝑐 > 𝑆𝑡ℎ 𝐷𝑐 > 𝐷𝑡ℎ 𝑆𝑐 < 𝑆𝑡ℎ 𝐷𝑐 < = 0 𝑆𝑐 > 𝑆𝑡ℎ 𝐷𝑐 > 𝐷𝑡ℎ 𝑆𝑐 > 𝑆𝑡ℎ 𝐷𝑐 > 𝐷𝑡ℎ 𝑆𝑐 < 𝑆𝑡ℎ 𝐷𝑐 < = 0 𝑆𝑐 > 𝑆𝑡ℎ 𝐷𝑐 > 𝐷𝑡ℎ 𝑆𝑐 > 𝑆𝑡ℎ 𝐷𝑐 > 𝐷𝑡ℎ 𝑆𝑐 > 𝑆𝑡ℎ 𝐷𝑐 > 𝐷𝑡ℎ

𝑆𝑎 𝑆𝑔 > 𝑆𝑔𝑡ℎ 𝑆𝑔 > 𝑆𝑔𝑡ℎ 𝑆𝑔 > 𝑆𝑔𝑡ℎ 𝑆𝑔 > 𝑆𝑔𝑡ℎ 𝑆𝑔 > 𝑆𝑔𝑡ℎ 𝑆𝑔 > 𝑆𝑔𝑡ℎ 𝑆𝑔 < 𝑆𝑔𝑡ℎ 𝑆𝑔 < 𝑆𝑔𝑡ℎ 𝑆𝑔 < 𝑆𝑔𝑡ℎ 𝑆𝑔 < 𝑆𝑔𝑡ℎ

3.2.2. Choosing the Appropriate Mother Wavelet The core of proposed scheme is the used mother wavelet. It is very important to choose an appropriate mother wavelet. The accuracy of this process is based on the smoothness of the mother wavelet selected. As the number of vanishing moments of the selected wavelet function increases, a more accurate representation of the distorted signal is obtained, in addition to that, greater smoothness can be achieved. This will provide a sharper cutoff frequency to the selected mother wavelet and reduce the amount of leakage energy to the adjacent resolution levels. In this regard, the db10 mother wavelet has been chosen to be used by the proposed scheme for FD, FC and FSI based on previous simulation studies. Also, the number of vanishing moments of the db10 wavelet is bigger than db8 and db4; therefore, it gives a meaningful wavelet spectrum of the analyzed signal. Hence, wavelet functions with a large number of coefficients will have less distortion than wavelets with fewer coefficients [50]. Besides, the db10 mother wavelet has an attribute of optimal asymptotic frequency localization, which gives a better time-frequency resolution. 3.2.3. Adjusting the threshold value Defining the threshold value is like configuring the settings of the relay. Extensive simulation studies have been done in previous works to determine the threshold value of the power network shown in Figure 2, while noticing the Sa, Sb, Sc coefficients of current signals. For instance, by creating - 11 -

different types of faults with different fault parameters. The adjusting adaptive threshold value is based on the following equation: 𝑆𝑡ℎ = 1.6 (𝑆𝑎 + 𝑆𝑏 + 𝑆𝑐)

(3)

The protection scheme will continuously check the difference between the stored load current and the rms current and also the detailed coefficients of current signals (𝐷𝑎, 𝐷𝑏, 𝐷𝑐) in node [1, 1] to ensure the change in generating operating conditions. In such a scenario, the threshold (𝑆𝑡ℎ) will not be changed unless the new value is settled for a period of 3 consecutive cycles at the power frequency. 4.

Simulation study 4.1. Test system For the configuration system shown in Figure 2, simulation studies using ATP/EMTP on the case

studies tested are carried out at Sf of 6.4 kHz. The test system is a 400 kV, 300 km TL and a three-phase bank of series capacitors (SCs) installed at the mid-line for compensation. The compensation rate was assumed as 70%. Metal-oxide varistors (MOVs) are installed in parallel to the series capacitors and modeled as nonlinear resistors; their parameters are given in Table 4 [51]. B

A System A

System B

SCs Proposed Scheme

MOVs

Load 200MW

Air gap

Load 200MW

Fig. 2. Single-line diagram of the studied 400 kV double-ended line. Table 4 Parameters of the studied TL system System voltage Equivalent system at terminal A (φ=0°) Equivalent system at terminal B (φ= –15°)

Line AB

Series compensation MOV characteristic: 𝑉𝑉 𝑞 𝑖𝑀𝑂𝑉 = 𝑝 𝑉𝑟𝑒𝑓

( )

400 kV Z1SA

(0.656+j7.5) Ω

Z0SA

(1.167+j11.25) Ω

Z1SB

(1.31+j15) Ω

Z0SB

(2.33+j26.6) Ω

Line length Z1

300 km (0.028+j0.315) Ω/km

Z0

(0.275+j1.027) Ω/km

C1

13.0 nF/km

C0

8.5 nF/km

SCs Position of the capacitor bank p

0.70 X1L

Vref

150 kV

q

23

0.5 p.u. 1 kA

- 12 -

4.2. Cases under study The response of the proposed scheme was investigated ten times for the system shown in Figure 2. The main cases tested were generated by changing parameters such as the fault inception time, fault location and fault resistance under different system conditions. The main cases are illustrated in detail as examples in the following sections. The studied cases can be classified as follows to successively detect and classify faults and identify the fault zones: Case 1: Fault types, locations, fault time occurrence (inception angle) and fault resistance effects. Case 2: Variation of the settled normal load and changing the threshold value. Case 3: Effect of fault types and fault time occurrence on the FZI scheme. Case 4: Effect of change in SC location on the FZI scheme. Case 5: Variation of the compensation level (25% and 50%) on the FZI scheme. Case 6: Effect of Sf on the proposed scheme. Case 7: Effect of variation of voltage and frequency on the proposed scheme. Case 8: Effect of variation of source impedance on the proposed scheme. Case 9: Effect of DC offsets on the performance of the proposed scheme. Case 10: Effect of noise on the proposed scheme. Case 11: Effect of load variations. 5.

Response of the fault identification scheme 5.1. Simulation results: Case 1 Several test cases corresponding to the investigated case 1 are considered in this section to

determine the ability of the suggested scheme to detect and classify faults correctly. The current of each phase is analyzed by using WPT at level 7 to get the maximum absolute value for the approximation coefficient of the current signals in node [1, 0] and the maximum absolute value for the detailed coefficients of the current signals in node [1, 1]. It should be noted that the current of each phase is measured at one end. Figures 3 and 4 show the Sa and Sd indices for faults under different operating conditions. Figures 3a and 3b show the Sa and Sd indices for phase A at an AG fault at 20% of the line, assuming 50 Ω fault resistance. As we would expect, the Sa magnitude of the faulty phase is much higher than Sth. Figures 3c and 3d show the Sa and Sd indices for phases A and B at an ABG fault at 45% of the line, assuming 1 Ω fault resistance. Also, the magnitudes of the faulty phases are much higher than Sth.

- 13 -

4

3 x 10

600

Sa Sth

Da

400

Sa

2

200

1

0 0

0.05

0.1

0.15 Time (s)

0.2

0.25

0 0

0.3

(a) Sa for AG fault at 0.08 s

0.2

0.25

0.3

600 Da, Db

Sa, Sb

2

0 0

0.15 Time (s)

800

Sa Sb Sth

4

0.1

(b) Da for AG fault at 0.08 s

4

6 x 10

0.05

Da Db

400 200

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

(c) Sa, Sb for ABG fault at 0.11 s

0 0

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

(d) Da, Db for ABG fault at 0.11 s

Fig. 3. Response of the scheme under different fault types with different resistance; fault before the capacitor. Figures 4a and 4b show the Sc and Dc indices for phase C at a CG fault at 55% of the line, assuming 10 Ω fault resistance. In turn, the Sc magnitude of the faulty phase is much higher than Sth. Figures 4c and 4d show the Sa and Sc indices for phases A and C at an ACG fault at 85% of the line, assuming 30 Ω fault resistance. Also, the Sa and Sc magnitudes of the faulty phases are much higher than Sth. Moreover, many fault types covering the whole line length are observed. As presented in Table 5, it was found that the fault types are correctly identified in all the tested cases, in which a considerable difference between the healthy and faulted phases is observed for the different fault types. As seen from the results, the Sa index for the faults before and after the series compensation do not vary much, because it is calculated by taking only an approximate coefficient, which provides the features of low frequency components. To sum up, the magnitude of the healthy phase is always much lower than the faulted phases which validate the performance of the proposed scheme. Thus, one can say that a robust scheme for FD and FC which provides accurate results under different operating conditions is proposed in this paper.

- 14 -

Table 5 FD and FC results for different fault types Fault types

Fault location (%)

Fault resistance (Ω)

Fault time occurrence (s)

AG

10

1

0.071

BG

35

30

0.070

CG

40

50

0.064

ABG

55

150

0.063

BCG

60

20

0.065

ACG

75

1

0.076

AB

90

50

0.059

BC

20

40

0.061

AC

40

30

0.062

AG

60

120

0.070

BC

80

25

0.056

ACG

90

60

0.068

BG

75

10

0.075

ABC

45

0.5

0.070

ABCG

55

15

0.065

Base case (No fault)

-------

-------

-------

𝑆𝑎× 104

𝑆𝑏× 104

𝑆𝑐× 104

𝐷𝑎 2.52 540 0.31 0 0.30 0 1.86 650 0.31 0 1.986 670 1.85 588 0.32 0 3.12 553 1.985 538 0.31 0 1.65 668 0.32 0 2.86 593 1.962 623

𝐷𝑏 0.31 0 2.46 510 0.29 0 1.65 610 1.98 590 0.29 0 1.68 592 3.012 621 0.29 0 0.31 0 2.016 586 0.33 0 2.15 493 3.152 612 2.025 602

𝐷𝑐 0.30 0 0.32 0 2.60 490 0.29 0 1.69 625 2.012 610 0.31 0 2.99 568 2.89 532 0.29 0 1.986 605 1.75 609 0.31 0 3.242 609 1.865 642

0.302

0.300

0.301

0

0

0

𝑆𝑔

Fault classification result

7.35e+003

AG

8.12e+003

BG

8.26e+003

CG

7.68e+003

ABG

7.93e+003

BCG

7.52e+003

ACG

3.62e-004

AB

4.69e-004

BC

3.58e-004

AC

5.86e-004

AG

5.73e-004

BC

6.83e+003

ACG

7.56e+003

BG

4.98e-004

ABC

3.69e-004

ABCG

5.81e-004

Base case (No fault)

5.2. Simulation results: Case 2 Figure 5 shows the scheme of the maximum absolute value for the approximated coefficient of the current signals in node [1, 0] and the maximum absolute value for the detailed coefficient of the current signals in node [1, 1] under normal load changing and a three-phase short-circuit. Under normal load changing, it is obvious that there is no significant change in the detailed coefficient. Moreover, as the proposed index value does not remain above the threshold level for more than three cycles; no FD is achieved.

- 15 -

4

2 x 10

400

Sc Sth

300 Dc

1.5 Sc

1

200 100

0.5 0 0

0.05

0.1

0.15 0.2 Time (s)

0.25

0 0

0.3

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

(b) Dc for CG fault at 0.09 s

(a) Sc for CG fault at 0.09 s 4

2.5 x 10

500

Sa Sc Sth

400

1.5

Da, Dc

Sa, Sc

2

1

Da Dc

300 200 100

0.5 0 0

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

0 0

0.35

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

0.35

(d) Da, Dc for ACG fault at 0.15 s

(c) Sa, Sc for ACG fault at 0.15 s

Fig. 4. Response of the scheme under different fault types with different resistance; fault after the capacitor. It is obvious from the scheme’s performance that the considerable change in the rms current value is properly interpreted as the load increasing and so the threshold value will be altered to a new value once the new load value is kept at this condition for at least 3 periods. 800

10000

Sa Sb Sc Sth

Da, Db, Dc

4000 2000 0

0.05

Da Db Dc

600

6000

0.1

0.15 0.2 Time (s)

0.25

0.3

400 200 0 0

0.35

(a) Sa, Sb, Sc for load variation

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

0.35

(b) Da, Db, Dc for load variation

4

Sa Sb Sc Sth

3 2 1 0 0

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

(c) Sa, Sb, Sc for three-phase short-circuit

Da Db Dc

600

Da, Db, Dc

4 x 10

Sa, Sb, Sc

Sa, Sb, Sc

8000

400 200 0 0

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

(d) Da, Db, Dc for three-phase short-circuit

Fig. 5. Load variation and three-phase short-circuit.

- 16 -

5.3. Simulation results: Case 3 From a stability standpoint, FZI is an important duty for transmission lines. Fundamentally, a distance relay needs an FZI to discriminate the faults encountering and not encountering the series compensation to estimate the fault distance in the presence of series compensation at the midpoint of a line. In this work, for the transmission system considered, the WPT identifier should be able to distinguish faults within the series compensation and beyond it. The current of each phase is used to get Im as represented in Eq. (1), and then the mode current is analyzed by using WPT at level seven to get the energy values of nodes [7, 0], [7, 3], [7, 4], [7, 5], [7, 6], [7, 7], [7, 8], [7, 9] and [7, 10] and then to determine the FZ index. Obviously, the magnitude of the FZ index in the case of the fault after the compensator is higher than in the case of the fault before the compensator, in which the magnitude of FZ in the case of the fault before compensation is null. The significant difference between the two cases is related to the effect of the compensation device. Different fault types are examined. In all the cases, as observed from the relay point, the position of the fault whether before or after the SC is correctly identified as shown in Figure 6. 4

2 x 10

5000 After Before

4000

After Before

1.5

2000

0.5

1000 0

1

Fz

Fz

3000

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

0

0.35

0.05

0.1

(a) AG fault

0.15

0.2 Time (s)

0.25

0.3

0.35

(b) ABG fault 4

4 x 10

After Before

After Before

3 Fz

Fz

10000

2

5000 1

0

0.05

0.1

0.15

0.2 Time (s)

0.25

(c) BC fault

0.3

0.35

0

0.05

0.1

0.15

0.2 Time (s)

0.25

0.3

0.35

(d) ABCG fault

Fig. 6. Different fault types at fault length 45% and 55% from line with compensation level 70%. 5.4. Simulation results: Case 4 In this case, the SC was placed at the start and end of the line shown in Figure 2 to test the performance of the scheme against SC location variations. The AG fault type occurs in two cases for the SC located at the start and end of the line, i.e. the fault occurs in two cases, before and after the SC. Figure 7 shows different plots of the results obtained. It is clear that the proposed scheme is unaffected by the change in SC location and successfully identified whether the fault was before or after the SC. - 17 -

4

4000 After Before

2000 1000

x 10

After Before

1.5 Fz

Fz

3000

0

2

1 0.5

0.05

0.1

0.15

0.2 Time (s)

0.25

0.3

0.35

0

0.05

0.1

0.15

0.2 Time (s)

0.25

0.3

0.35

(b) SC located at end of the line

(a) SC located at start of the line

Fig. 7. AG fault type at different SC locations. 5.5. Simulation results: Case 5 In cases 1 to 5, the compensation level equal to 70% is used. The results obtained using this compensation level operation evidently illustrate the effectiveness of the relaying scheme. Further, to explore the effectiveness of the scheme against a change in the compensation level, the SC was next operated with a 25% and 50% compensation level. Figure 8 shows the performance of the proposed scheme under an ACG fault occurring before and after the SC with a 25% and 50% compensation level. The scheme was found to work correctly. 3x

4

4

2 x 10

10

After Before

Fz

Fz

2

1

0

After Before

1.5 1 0.5

0.05

0.1

0.15

0.2 0.25 Time (s)

0.3

(a) 25 % compensation level

0.35

0

0.05

0.1

0.15

0.2 0.25 Time (s)

0.3

0.35

(b) 50 % compensation level

Fig. 8. ACG fault type at different compensation levels. 5.6. Simulation results: Case 6 Case 6 presents the effect of the sampling rate on the performance of the proposed scheme. The sampling rate used is set as 6.4 kHz (128 samples/cycle) for a system operating at a frequency of 50 Hz, in which the maximum resolution level that can be reached is the 7th level, i.e. 2N= 128 =27. The proposed scheme was tested under a similar condition with a sampling rate = 3.2 kHz (64 samples/cycle). A BG fault type is produced. Figure 9 shows the performance of the proposed FD scheme for the two sampling frequencies, respectively. Figure 10 shows the performance of the proposed FZI scheme for the same two sampling frequencies for a CG fault occurring before and after the series capacitor.

- 18 -

6000

5000

5000

Sa

Sa

6000

4000

4000

3000 0

500 1000 Nimber of samples

3000 0

1500

(a) Sa index at Sf = 3.2 kHz (64 samples/cycle)

500

1000 1500 2000 Number of samples

2500

3000

(b) Sa index at Sf = 6.4 kHz (128 samples/cycle) 60

40

40

Sd

Sd

60

20

20

0 0

500 1000 Number of samples

0 0

1500

500

1000 1500 2000 Number of samples

2500

3000

(c) Sd index at Sf = 3.2 kHz (d) Sd index at Sf = 6.4 kHz Fig. 9. Performance of the proposed FD scheme under different sampling frequencies.

10000

10000 After Before

8000

After Before

8000 6000

Fz

Fz

6000 4000

4000

2000

2000

0

200

400

600 800 1000 Number of samples

1200

1400

0

500

1000 1500 2000 Number of samples

2500

(a) FZ index at Sf = 3.2 kHz (b) FZ index at Sf = 6.4 kHz Fig. 10. Performance of the proposed FZI scheme under different sampling frequencies. As shown in both figures, the accuracy of the proposed FD scheme is independent of the sampling frequency. But it is important to note that the sampling rate should be equal to at least 1.6 kHz, which means that the maximum resolution level that can be met to determine the proposed indices is the 5th level. 5.7. Simulation results: Case 7 The proposed protection scheme is tested under variations of the operating voltage and frequency. In this test, +/-10% range is used for voltage variation and +/-0.5% range is used for the frequency variation. Table 6 shows the results obtained. It is obvious from the scheme’s performance the effectiveness of the scheme proposed for FD and FC of shunt faults in this case.

- 19 -

Table 6 FD and FC results under variation of the operating voltage and frequency Frequency (Hz)

Voltage (kV)

Fault types

Fault location (%)

Fault resistance (Ω)

50

380

AG

12

10

52.5

390

BG

50

1

47.5

420

CG

90

0.1

52.5

410

ABG

80

50

47.5

375

ACG

75

10

50

430

BCG

25

15

47.5

400

AB

65

50

50

385

BC

85

10

52.5

400

AC

95

1

51

390

ABCG

50

20

49

420

AG

85

10

52.5

380

BC

40

50

48.5

400

ABC

10

1

𝑆𝑎× 104

𝑆𝑏× 104

𝑆𝑐× 104

𝐷𝑎 2.71 580 0.33 0 0.32 0 2.51 630 2.68 620 0.33 0 2.53 610 0.33 0 2.69 610 2.64 650 2.61 701 0.32 0 2.72 620

𝐷𝑏 0.32 0 2.55 595 0.29 0 2.58 590 0.32 0 2.72 580 2.51 630 2.70 550 0.32 0 2.55 670 0.32 0 2.65 620 2.70 600

𝐷𝑐 0.31 0 0.29 0 2.61 650 0.32 0 2.65 590 2.71 560 0.29 0 2.72 570 2.64 580 2.65 630 0.31 0 2.64 590 2.71 580

𝑆𝑔

Fault classification result

7.98e+003

AG

8.58e+003

BG

7.52e+003

CG

8.69e+003

ABG

9.01e+003

ACG

8.92e+003

BCG

6.38e-004

AB

5.82e-004

BC

6.35e-004

AC

5.01e-004

ABCG

7.98e+003

AG

7.58e+003

BC

6.53e-004

ABC

5.8. Simulation results: Case 8 The proposed protection scheme is also tested under variation of the source impedance. In this test, +/-10% range is used in variating the impedance of the generating units. Table 7 shows the results obtained, which validate the robustness of the scheme suggested for FD and FC of shunt faults in this case. 5.9. Simulation results: Case 9 The performance of the proposed scheme has been analysed and verified in the presence of DC offsets, in which AG fault type occurred with fault inception angle equals to zero for phase A. Figure 11a shows the current signal in conjunction with DC offset. Approximate coefficients for phase A in node [1, 0] considering the DC offset are shown in Figure 11b. Figure 11c shows the effect of the DC offset on the detail coefficients for phase A in node [1, 1]. It can be observed that the fault index (Sa) in case of the DC offset is greater than the threshold. This means that the scheme proposed did not experience any adverse impact in response to this case.

- 20 -

Table 7 FD and FC results under variation of the source impedance. Fault location (%)

Fault resistance (Ω)

AG

5

10

1.31+j15

BG

50

1

0.593+j6.75

1.17+j13.5

CG

90

50

0.724+j8.25

1.44+j16.5

ABG

20

1

0.091+j2.59

1.31+j15

ACG

40

40

0.593+j6.75

1.17+j13.5

BCG

60

1

0.724+j8.25

1.44+j16.5

AB

80

25

0.091+j2.59

1.31+j15

BC

10

30

0.593+j6.75

1.17+j13.5

AC

5

60

0.724+j8.25

1.44+j16.5

ABCG

95

40

0.091+j2.59

1.31+j15

AG

60

35

0.593+j6.75

1.17+j13.5

BC

40

1

0.724+j8.25

1.44+j16.5

ABC

5

25

Impedance Z1sA (Ω)

Impedance Fault types Z1sB (Ω)

0.724+ j8.25

1.44+j16.5

0.091+j2.59

𝑆𝑎× 104

𝑆𝑏× 104

𝑆𝑐× 104

𝐷𝑎

𝐷𝑏

𝐷𝑐

2.69 630 0.32 0 0.33 0 2.72 690 2.58 650 0.31 0 2.57 720 0.31 0 2.68 680 2.57 690 2.61 650 0.30 0 2.71 690

0.31 0 2.64 590 0.32 0 2.71 710 0.33 0 2.59 700 2.60 680 2.71 650 0.29 0 2.59 680 0.31 0 2.58 680 2.70 670

0.32 0 0.30 0 2.61 710 0.31 0 2.58 620 3.01 650 0.31 0 2.70 670 2.69 700 2.60 700 0.33 0 2.59 670 2.72 700

Fault classification result

𝑆𝑔

7.98e+003

AG

8.58e+003

BG

7.52e+003

CG

8.69e+003

ABG

9.01e+003

ACG

8.92e+003

BCG

6.38e-004

AB

5.82e-004

BC

6.35e-004

AC

5.01e-004

ABCG

7.98e+003

AG

7.58e+003

BC

6.53e-004

ABC

4

Phase A current

3

x 10

2 1 0 -1 -2 0

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

0.35

(a) Phase A current signal with high DC offset 4

x 10

700

Sa Sth

4

600 500

Da

Sa

3 2

300 200

1 0 0

400

100

0.05

0.1

0.15 0.2 Time (s)

0.25

(b) 𝑆a for AG fault

0.3

0.35

0 0

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

0.35

(c) 𝐷𝑎 for AG fault

Fig. 11. DC offset effect on performance of the proposed protection scheme.

- 21 -

5.10. Simulation results: Case 10 Performance of the proposed protection scheme has been tested during a noisy condition, in which the fault signals captured are contaminated with white Gaussian noise. A signal-to-noise ratio (SNR) of 30–60 dB has been considered, in which BG fault at 75 km with 10 Ω fault resistance from bus A was selected to perform the noise test. Figure 12a shows the current signal (blue dashed line) in conjunction with noised current signal (red line). The approximate coefficients with the noise effect considered of phase B in node [1, 0] is shown in Figure 12b. Figure 12c shows the detail coefficients with the considered noise effect of phase B in node [1, 1]. It can be observed that the fault index, Sb, in case of

Phase B current (A)

noise is larger than the threshold value.

10000 5000 0 -5000 0.06

0.07

0.08

0.09 0.1 Time (s)

0.11

0.12

0.13

(a) Current signals of phase B with and without noise

4

2

With noise Without noise

x 10

250

Sb Sth

1.5

200

Db

Sb

150

1 0.5 0 0

100 50

0.05

0.1

0.15 0.2 0.25 Time (s)

0.3

0.35

(b) Sb for BG fault with noise

0 0

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

0.35

(c) Dbfor BG fault with noise

Fig. 12. Performance of the proposed protection scheme with noise considered. 5.11. Simulation results: Case 11 The load variation is a normal phenomenon in power systems. Therefore, 25% of the load connected at Bus A is suddenly increased to test the functionality of the proposed scheme in such a condition. The indices calculated are presented in Figure 13. Under normal load change, it is obvious that there is no significant change in the detailed coefficient and no FD is achieved. This means that the proposed scheme does not affect by such load variations. This is because the proposed protection scheme does not depend on the loads to detect faults but on the frequency content of the current signals.

- 22 -

5000

800

Sa, Sb, Sc

Da, Db, Dc

600

Sa Sb Sc

4500

Da Db Dc

400 200

4000 3500 3000 2500

0 0

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

2000 0

0.35

(a) Da, Db, Dc for load variation

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

0.35

(b) Sa, Sb, Sc for load variation

Fig. 13. Load variation effect on the performance of the protection scheme. 6.

Generalization of the scheme proposed

The proposed protection scheme can be extended for any transmission system. As a part of generalization, the proposed protection scheme has been applied to a multi-machine (WSCC 3machine) standard power system with series compensation, where its 9-bus configuration is shown in Figure 14. It should be noted that a modification has been incorporated by providing 40% compensation at the middle of line 7–8. The main parameters of the WSCC 9-bus system are given in [38]. The protected line with the proposed scheme connected (between buses 7 and 8) is shown in Figure 14. 8

7 Proposed scheme F

2

Generator 2

9

Load C

3

SCs F

TR 2

TR 3

MOVs

Generator 3

Air gap

6

5

Load A

Load B

4

TR 1 1

Generator 1

Fig. 14. Single-line diagram of the modified WSCC 9-bus system. 6.1. Fault detection and classification Several studied cases have been simulated to validate the capability of the proposed scheme for fault detection and classification in different fault situations. The fault situations investigated include - 23 -

different fault occurrence instants and resistances. Also, different fault locations (between buses 7 and 8) are implemented to validate the performance of the proposed algorithm as shown in Table 8. As expected, the proposed scheme will detect the faulty phases. Table 8 FD and FC results for different fault types Fault types Fault location (%) Fault resistance (Ω)

Fault time occurrence (s)

AG

20

10

0.063

BG

10

25

0.064

CG

90

60

0.070

ABG

5

100

0.071

BCG

30

10

0.062

ACG

60

0.1

0.069

AB

75

50

0.072

BC

95

80

0.064

AC

10

0.5

0.065

AG

40

1

0.062

BC

55

90

0.072

ACG

75

25

0.069

BG

85

40

0.075

ABCG

45

1

0.074

𝑆𝑎 × 104 𝐷𝑎 1.62 400 0.39 0 0.39 0 1.72 430 0.43 0 2.31 370 1.74 340 0.37 0 2.01 370 2.3 400 0.38 0 2.05 385 0.41 0 2.02 390

𝑆𝑏 ×104

𝑆𝑐 ×104

𝐷𝑏 0.4 0 1.83 380 0.4 0 1.76 510 1.63 430 0.42 0 1.81 480 1.85 370 0.38 0 0.42 0 1.95 355 0.36 0 1.87 380 1.92 410

𝐷𝑐 0.38 0 0.4 0 1.47 410 0.42 0 1.39 450 1.11 405 0.38 0 1.76 350 1.99 420 0.38 0 1.84 370 1.94 420 0.38 0 1.94 385

𝑆𝑔

Fault classification result

7.23e+003

AG

8.64e+003

BG

4.38e+003

CG

5.97e+003

ABG

3.78e+003

BCG

6.68e+003

ACG

5.98e-004

AB

8.68e-004

BC

6.89e-004

AC

3.87e-004

AG

5.95e-004

BC

4.98e+003

ACG

4.28e+003

BG

3.52e-004

ABC

6.2. Fault zone identification The simulation results shown in Figure 15 validate the applicability of the proposed scheme for FZI in case of WSCC 3-machine system. Thus, based on the knowledge gained from the several tests performed, the following can be noted: 

The current of each phase is used to get Im and then the mode current is analyzed by using WPT at level seven to get the energy values of nodes [7, 0], [7, 3], [7, 4], [7, 5], [7, 6], [7, 7], [7, 8], [7, 9] and [7, 10] and then to determine the FZ index.



The magnitude of FZ in the case of the fault after compensation is higher than in the case of the fault before compensation, in which the magnitude of FZ in the case of the fault before compensation is null. The significant difference between the two cases is related to the effect of the compensation device.



Different fault types are examined as shown in Figure 15. In all the cases, as observed from the relay point, the position of the fault whether before or after the SC is identified correctly. - 24 -

2500 4000

After Before

2000

After Before

Fz

Fz

3000

1500 1000

1000

500 0

2000

0.05

0.1

0.15 0.2 Time (s)

0.25

0.3

0.35

0

0.05

0.1

(a) AG fault

0.15 0.2 Time (s)

0.25

0.3

0.35

(b) BCG fault

Fig. 15. Different fault types at fault length 45% and 55% from line at WSCC 3-machine. 7.

Comparison with other schemes presented in the literature A comparative study between the proposed scheme and other schemes in the literature is

presented in Table 9. The authors in [6], [7], [8], [10] and [40] used a fixed threshold value for faults identification, which has the limitation that, when applying the scheme in another system with a different voltage range, a new threshold should be determined. However, to solve this problem, in this work, the threshold value is adaptive and is readjusted according to the load changing and the status of the power system, without any human interaction being required. The techniques in [19], [21], [23] and [26] are dependent on samples and knowledge representation training, resulting in a complicated task. Also, they are not able to manage the uncertainties in the transmission system, which will affect the reliability of FD and FC and FZI. The TW needs a high Sf rate, leading to a high cost and requiring specially designed transducers [5], [42], [43] and [44]. The two methods in [35], [39] and [40] were dependent on communication, which suffers from the lack of reliability in communication systems that exists in practice. Besides, the proposed protection scheme is compared with a commercially protective relay, called ABB 670 series presented in [52]. The ABB 670 series relay is based on DFT to analyze the fault signal, while the proposed protection scheme is based on WPT to analyze the fault signal. As known, the DFT is a widely used method for feature extraction. However, its major drawback is that it assumes that the fault signal is stationary and it also eliminates the time-frequency information of the signal. Moreover, most signals contain numerous non-stationary or transitory characteristics: drift, trends, and abrupt changes, in addition to beginnings and ends of events. These characteristics are often important parts of the signal, and the Fourier analysis is not suited to detect them [53]. To overcome the limitation of the DFT, the proposed scheme used the WPT, in which the WPT decomposes the signal into two components: high-frequency and low-frequency bands in the time-frequency domain. WPT has some unique features that make it more suitable for transient signal analysis in power systems [54], such as:  The time-domain information is not lost when it is used to extract the signal components.  It has a good performance even in case of a small disturbance. - 25 -

As well, the proposed protection scheme is compared with another commercial protective relay, SEL-T400L time-domain line protection [55]. In SEL-T400L relay, the fault type identification unit is based on incremental quantities, which use the differences between the instantaneous voltages, currents and their one-cycle-old values. But the proposed protection scheme is deterministic and independent of the system; therefore, it avoids the need for collecting historical data. Table 9 Detection protection schemes compared to the scheme proposed Technique

Process type

Proposed WPT technique

Directly on modal current signal High frequency components of current Directly on SE for modal current Directly on WE for current coefficients Directly on current coefficients

WT & SD [6] DWT [7] DWT & WE [8] DWT [10] WT & PNN [19] DWT & SVM [23] DWT & MCSVM [26]

WT, PNN & TW [43] TW, SVM & MMG [44]

Coefficients of voltages and currents

WT & TWs [5] WT & TWs [42]

[35] Average value [39] [40]

8.

Directly on DC component Superimposed components of voltage and current RPF & positive sequence voltage and current

Communication

Phase current signals from one end

Directly on low and high frequency components of currents Approximated and detailed coefficients of currents Directly on SE for phase voltages Modulus maxima of wavelet coefficients at high scales Detailed coefficients of voltages

DWPT, ChNN & SVM [21]

Input data

No

Phase voltage signals from one end

Phase current and voltage signals from one end Phase current signals from two ends Phase current and voltage signals from two ends

Yes

FD and FC

FZI

Sf (kHz)

Setting threshold

√

√

6.4

Adaptive

√

√

10

√

√

200

√

√

10

√

×

Not reported

√

×

20

×

√

4

√

×

1.6

√

×

4

√

×

80

√

√

400

√

×

100

√

×

10

×

√

Not reported

√

√

3.2

√

√

1

Fixed

No need

Fixed

Conclusion and future works

In this work, an adaptive WPT-based protection scheme is proposed for a SCTL. The proposed scheme provides FD and FC and FZI by analyzing the phases current using WPT. The test results validated the effectiveness of the proposed scheme for any fault type and position. The novelty of the proposed

- 26 -

scheme and the most important attributes that demonstrate its effectiveness in comparison with previous schemes are briefed as follows: 

The proposed scheme for FD, FC and FZI does not need awareness of the fault ignition time.



The proposed protection scheme is deterministic and independent of the system thus it avoids the need for collecting historical data.



The proposed scheme employs an adaptive threshold level and therefore no special adjustment is needed for different transmission systems.



As the proposed scheme involves only a small amount of computation, this enables very fast and accurate protection measures for the SCTLs.



The proposed protection scheme can reduce the cost associated with protection equipment as it uses measurements of only one end of the system.



For the FD and FC and FZI functions, the same feature extraction stage is applied in the proposed protection scheme, thereby improving its operation speed and making the proposed scheme easier to implement compared with the competitive schemes in the literature.



Additional artificial intelligence techniques are not needed for support in the proposed scheme, resulting in a simplified scheme compared with the competitive schemes in the literature.



The robustness of the proposed protection scheme is evaluated by different positions and different compensation levels of the series capacitor in the transmission line. Finally, we should point out that other factors that were beyond the framework of the study, and

will be included in future studies, are considering the power quality issues and studying the behavior of the proposed scheme in case of single pole tripping, and power swing condition. Acknowledgements The authors thank the editor and the anonymous reviewers for their constructive comments and suggestions.

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Highlights 

Various methods applied for series-compensated transmission lines (SCTL) are discussed.



An investigation of solutions to their drawbacks is presented.



A novel scheme based on the application of wavelet packet transform is proposed for an SCTL.



Simulation results validate the effectiveness of the proposed protection scheme.

Conflict of Interest and Authorship Conformation Form Please check the following as appropriate:

o

All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version.

o

This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue. - 32 -

o

The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript

o

The following authors have affiliations with organizations with direct or indirect financial interest in the subject matter discussed in the manuscript:

Author’s name

Affiliation

Ahmed R. Adly Assistant professor at Nuclear Research Center, Atomic Energy Authority, Cairo, Egypt Shady H. E. Abdel Aleem 15th of May Higher Institute of Engineering, Mathematical and Physical Sciences Department, Helwan, Cairo, Egypt Mahmoud A. Elsadd Faculty of Engineering, Menoufia University, Egypt Ziad M. Ali Electrical Engineering Department, College of Engineering at Wadi Addawaser, Prince Sattam bin Abdulaziz University, Saudi Arabia

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