Combined DFT and Fuzzy Based Faulty Phase Selection and Classification in a Series Compensated Transmission Line

,e conventional distance protection scheme malfunctions sometimes in case of a fixed series capacitor compensated transmission line due to the change in relaying impedance of the protected line during faulty conditions. In order to mitigate this problem, a combined discrete Fourier transform and fuzzy (CDFTF) based algorithm has been proposed in this paper. ,is method has been tested on a 400 km, 735 kV series compensated transmission line network and WSCC 3-machine 9-bus system for all fault types using MATLAB/Simulink and PSCAD platforms, respectively. A fixed series capacitor is located at the middle of the protected line. ,e fundamental components of phase currents, phase voltages, and zero-sequence current are fed as inputs to the proposed scheme. ,e fault detection, faulty phase selection, and fault classification are achieved within 1/2–1 cycle of power frequency. ,e proposed CDFTF-based scheme is less complex and is better than other data mining techniques which require huge training and testing time. Test results corroborate the proposed scheme reliability with wide variations in fault location, fault resistance, fault inception angle, evolving faults, compensation level, and heavy load interconnection. ,e results discussed in this work indicate that the proposed technique is resilient to wide variations in fault and system conditions.


Introduction
e primary reasons behind adoption of a series capacitor in the long transmission line include increased transmittable power, improved transient stability, voltage stability, power oscillation damping, and thereby reduced transmission and revenue losses.When the power system is subjected to a short circuit fault, it is accompanied by flow of huge fault current which may damage of the connected equipments and also create power quality problems.erefore, accurate fault detection and classification are very crucial tasks in power system protection to restore the power supply and to improve the reliability.e installation cost of SCs is also less for 15-30% compensation as compared to installation/ erection of a new line, and also it is not affected by environmental concerns [1,2].Distance relays used for the protection of a fixed series compensated line may experience overreach during a fault due to the involvement of the series capacitor in the fault loop, and also the distance function may fail to pick up a low fault current in the protected line.
e distance relay protects 80-85% of the transmission line length, and it operates based on the impedance seen by relay location.
e inclusion of a capacitor in the line either compensates or cancels a part of the transmission line inductance, which may result in a fault seen by the relay in its 1st zone although the fault has actually occurred in the 2nd or 3rd zone of protection.Similarly, a fault in the 1st zone can be perceived to be a fault in the reverse direction.For proper isolation of the faulty phase(s), correct knowledge of the faulted phase(s) is essential.Fast and reliable fault detection and classification technique is an important requirement in power transmission systems to maintain continuous power flow [3].If the transmission line is series compensated, this task becomes more complicated.
Various schemes have been proposed earlier for fault classification in uncompensated and compensated transmission lines.
ese algorithms usually require measurements at one end or two ends of lines.To complement the existing methods, a sequence component-based method is proposed in [4].In [5], decision tree-based fault classification is proposed for a transmission line compensated by a fixed series capacitor.Phase selection based on superimposed voltages and currents under balanced load is proposed in [6].Faulty phase selection based on an integrated moving sum approach is proposed for SCTS in [7].
e authors of [8,9] have developed fault classification algorithms using artificial neural networks (ANNs), but sometimes ANN-based approaches are subjected to underfit and overfit problems and may also stuck in a local minima.Methods based on adaptive neurofuzzy (ANFIS) for fault classification in the long transmission line have been proposed in [10,11].In [12][13][14], a support vector machine (SVM) has been used to classify the fault, but the schemes based on machine learning techniques require huge computational burden and are quite complex.In [15][16][17][18], fault classification schemes based on fuzzy logic have been presented with different feature extraction techniques such as discrete Fourier transform [15], wavelet transform [16], higher order statistics [17], and angular differences among the sequence components of the fundamental currents [18].Fault classification technique based on probabilistic neural networks (PNNs) is discussed in [19].In [20], the authors have conferred the effectiveness of an extreme learning machine for the protection of a long transmission line.Cross-country faults and evolving faults have been investigated in [21].Furthermore, hyperbolic S-transform and support vector regression method have been developed for protection of series compensated lines in [22].In [23], an intelligent relaying scheme based on decision tree (DT) has been validated in the real-time digital simulator (RTDS).Recently, discrete wavelet transform and k-nearest neighbour have been used for fault detection, classification, and location estimation in a double circuit series compensated line in [24].
e main challenges in fault classification in an extrahigh-voltage (EHV) series compensated transmission line are as follows: (a) e conventional distance relay employed in an EHV transmission line may mal-operate during stressed conditions such as load variation, power swing, load encroachment, and system frequency variation.Also the distance relay underreaches and overreaches during high-resistance fault and fault with high DC offset current.(b) Series capacitor is a popular device to increase the current carrying capacity of a transmission line by reducing the effective length of line.Change in the line current and voltage affects the seen impedance by the conventional distance relay.Moreover, it may result in voltage or current inversion and hence result in malfunction of the relay for certain types of faults [2].(c) Moreover, it is required to have two separate algorithms to deal with faults occurring before series capacitor and after series capacitor.
(d) Presence of a metal oxide varistor (MOV) and bypass switches may also lead to the challenges [2] in protection of transmission lines.MOVs change the effective impedance of the installation depending on the degree of MOV conduction, which is nonlinear.
is paper aims to validate the CDFTF-based approach for classification of all the shunt faults in a series compensated system.Feasibility of the proposed CDFTF-based scheme has been tested on a 735 kV, 60 Hz, and 400 km long transmission system and a modified WSCC 3-machine 9-bus system which is a midpoint-fixed series capacitor compensated in MATLAB/Simulink [25]and EMTDC/PSCAD platforms, respectively.e main novelty of the proposed work can be explained as follows: (a) e proposed scheme is very simple and easy to implement as it uses the fundamental phasor of the signals at one end only and then it applies the Fuzzy approach to make the final decision.(b) In the proposed scheme, one single Fuzzy-based relay can detect and classify the fault either before or after the series capacitor, whereas in the existing scheme two separate algorithms are required.(c) ere is no requirement of a communication channel between two ends and hence the reliability is improved, and furthermore cost and computation burden is reduced.(d) e speed of the presented relaying scheme is within half cycle of power frequency (i.e., less than 10 ms).(e) e proposed scheme works well for an evolving fault and heavy load interconnection.(f ) Efficacy of the proposed scheme is also validated on a modified WSCC 3-machine 9-bus series compensated network and provides an average accuracy of 99.678%.
e paper is divided into six sections.Section 2 gives a brief overview of the series compensated transmission system.In section 3, the CDFTF-based scheme is discussed.In section 4, it illustrates the performance of the proposed algorithm under different fault scenarios.In section 5, it compares the proposed with earlier reported schemes.In the final section, the concluding remarks have been given.

Series Compensated Transmission System (SCTS)
e single-line diagram of 735 kV, 60 Hz SCTS is shown in Figure 1.It consists of a doubly-fed series compensated transmission system wherein source 1 is a power plant consisting of six 350 MVA generators and source 2 is a evenin equivalent source of the interconnected grid.e line 1 between bus B3 and bus B2 has 100 km length while the line between bus B4 and B2 has 300 km length.Further to enhance the power transmission capability of the system, the 300 km line 2 between buses B4 and B2 is the midpoint compensated by a fixed series capacitor of 62.8 µF in each 2 Modelling and Simulation in Engineering phase representing 40% compensation of the reactance of line 2. e SC is protected by the MOV block which consists of 60 columns, and its protection level is set to 238.9 kV. is voltage corresponds to 2.5 times the nominal capacitor voltage.All fault simulation studies have been carried out using the MATLAB/Simulink platform [25].SC is protected by MOV overvoltage and the air gap.For simulation studies, a sampling frequency of 1.2 kHz is chosen.Figure 1 shows a schematic diagram of the simulated system.
e system parameters are given in Appendix A.

Proposed CDFTF-Based Fault Classification Scheme
In this work, combined DFT and fuzzy logic technique based on the fault classification scheme has been proposed for a series compensated transmission system.Figure 2 presents the flow chart of the proposed CDFTF-based technique.e fundamental component magnitude of 3-phase voltages and currents are obtained after preprocessing the single-end measurements.In the preprocessing stage, the 3-phase time domain (instantaneous) voltage and current signals are converted into discrete samples through zero-order hold block with a sampling frequency of 1.2 kHz and passed through a 2nd-order low pass Butterworth filter with a band pass edge frequency of 2 * pi * 400 rad/s.Furthermore, the filtered discrete 3-phase signals are passed through the recursive discrete Fourier transform (DFT) block available in MATLAB/Simulink to obtain the fundamental components of voltages and currents in the time domain.For knowledge of the ground involvement in the fault, a sequence analyzer is used to calculate the magnitude of zero-sequence current.
After preprocessing, the fundamental component magnitude of 3-phase currents and voltage signals are applied to the proposed fuzzy-based fault classification algorithm.Fuzzy logic is an extension of multivalued logic and problem solution methodology which gives a better and precise conclusion from vague and imprecise data.Basically, fuzzy logic has four stages: (i) fuzzification; (ii) inference system; (iii) fuzzy rule base/knowledge base; and (iv) defuzzification.In fuzzification, crisp inputs are converted into fuzzified inputs, which are processed by the inference system according to the rules defined in the rule base/ knowledge base.e decision taken by the inference system is fuzzy in nature which cannot be understood by the real-time system, so this is mapped into crisp output through the defuzzification stage.e membership function shape is very important with respect to the performance of the whole system.In this work, the triangular membership functions for fuzzification and the centroid method for defuzzification have been chosen.Figure 2 presents the flow chart of the proposed CDFTF-based technique.
During the fault in the forward direction, only fuzzybased fault classifier is activated which determines the types of faults along with the phase(s) involved.Inputs for the FFC are the magnitudes of fundamental voltage and current.e fuzzy based fault classifier (FFC) is designed separately for each phase and also for ground identification.
Based on the type of fault that has occurred in the line, corresponding faulted phase(s) and ground output become high (1) and healthy phase(s) output remains low (1).us, both the faulty phase(s) and the type of fault are identified using the proposed scheme as exemplified in Figure 2.About the ground involvement, the magnitude of zero-sequence current is taken.For identification and classification of faulty phase(s), the fundamental component of voltage and current using DFT is considered as input.e zero-sequence current signal is obtained using the sequence analyzer in order to determine the ground involvement.
Steps to design the fuzzy rules are as follows: (a) Simulate all ten types of faults in the MATLAB/ Simulink model of the test system at 10 km and 290 km from the relaying bus with the variation in fault resistance (i.e., 10 Ω and 100 Ω) and fault inception angle (0, 45, 90, and 270).  1 and 2.
Each voltage and current signal is divided into three ranges with triangular membership function (TMF): low, medium, and high, as described in Table 2. FFC provides four outputs corresponding to the three phases, namely, "phase A," "phase B," "phase C," and "ground G" which goes high (1) in the case of fault occurrence or else remains low (0) during healthy conditions.Output trip logic also consists of two ranges, namely, trip low TL (0) and trip high TH (1).
e effect of variations on different fault factors has also been studied, such as fault type, fault location, fault resistance, fault inception angle, evolving fault, compensation level, etc.As illustrated in Figure 2, if a fault occurs in the protected zone, three-phase voltage and current signals are acquired at the relay point which will be further preprocessed by fullcycle DFT for the feature extraction process.e sampling frequency for the collected signal is kept to be 1.2 kHz.To know the ground involvement, the zero-sequence component of the current signal has been calculated.Extracted features of voltage and current signals, i.e., fundamental components, are fed to the fuzzy module of phase(s).FFC deliver the four outputs A, B, C, and G which are declared as "zero" in the case of "no fault" and otherwise "one." In this paper, we have used TMF as shown in Figure 3 which is specified by three parameters {P, Q, R} whose values have been taken as described in Table 2 for phase(s) as well as for ground detection and classification.
e rule base designed for ground detection is as follows: (i) If zero-sequence current is I LOW or I MID , then the trip is TL (ii) If zero-sequence current is I HIGH , then the trip is TH Detection and classification time of the relay for faulty phase(s) can be calculated as follows: where T r , T o , and T i stand for the response time taken by the relay to classify the faults, the relay operating time, and the time of inception of a fault, respectively.From Table 3, it is clear that the time taken to classify phase(s) and ground is less than half cycle in almost all of the fault cases.e SCTS has been simulated using MATLAB/Simulink software.e aim of this study is to validate various fault circumstances, and a huge fault dataset has been considered with wide variations in fault parameters, such as fault location (FL), fault resistance (FR), fault inception angle (FIA), and fault type (FT) under wide variations in system conditions.e different system conditions have been generated with various compensation levels.e values of the fault parameters considered in this paper are as follows:

Performance Evaluation of the Proposed Scheme
To evaluate the effectiveness of the CDFTF-based scheme, a 735 kV, 60 Hz 3-phase series compensated transmission system (SCTS) with a distributed line model as shown in Figure 1 has been considered and simulated in the MATLAB/Simulink environment.e system details have been provided in Appendix A. During normal system condition, power flow takes place from Bus B1-B2.e voltage and current signals are acquired at the relaying point, i.e., at Bus B4. e sampling rate for the collection of voltage and current signals is maintained at 1.2 kHz.

Effect of Fault Location.
e effect of variations in the fault location on the performance of the presented scheme has been analyzed with varying resistance in the range of 0.001 Ω to 50 Ω for all shunt faults.Test results of the variations in fault locations are summarized in Table 4. Figures 4(a 5 summarizes the performance of the proposed scheme, which presents the time required to classify the fault(s) that is considerably less than half cycle of power frequency in most of the cases.

Effect of Fault Inception Angle.
Faults in a transmission line can occur at any time instant.So, the proposed CDFTFbased method has also been tested for varying FIA, and results have been presented in Table 6.For all the tested cases, the response time for classification of faults is within one cycle of power frequency in most of the cases.Fault

Effect of Fault
Type. e proposed CDFTF-based method also helps in identifying and classifying the faulty phase(s) with the variation in shunt fault types.Basically, there are 10 fault types that involve all combinations of A, B, C, and G.All FTmust be applied to test the ability of the relay for accurate classification of the faulty phase(s).Some of the results are tabulated in Table 7. e response time of the presented CDFTF-based relay with wide variations in fault types is included in Table 7.
Figures 7(a) and 7(b) show the graphical time domain 3phase voltage and current signals at relaying bus B4 for an AG fault including FIA � 45 °and FR � 50 Ω at 50 km.Figure 7(c) shows the output of FFC in which phase A and ground G go high (1) at 0.5058 sec and 0.5050 sec, respectively, and all other phases remain low (0), clearly indicating the occurrence of AG fault.Hence, it can be inferred that the proposed technique is capable of classifying faults in less than half cycle in most of the cases.

Effect of Evolving Faults.
e effectiveness of the proposed CDFTF-based technique has been examined for Modelling and Simulation in Engineering evolving faults.An evolving fault can be defined as a fault where the involvement of phases changes over a period of time.For example, an evolving fault begins as a single lineto-ground fault, and after a short time interval, it transforms into a double line-to-ground fault [21].e characteristic of an evolving fault is that its faulted phases change over time, while other types of faults' faulted phases remain unchanged.e effectiveness of the presented scheme during evolving faults has been examined, and some of the results are presented in Table 8.From Table 8, it can prove that the proposed CDFTF-based method can classify the evolving faults correctly within half cycle in most of the conditions.Figures 8(a    of 50 Ω just after the initiation of an initial fault.e time deviations between the two faults are 26 ms.In Figure 8(c), it is clearly examined that the faulty phases B and C and ground G become high (1) after fault inception with phase A remaining low (0).Proposed schemes correctly classify the faulty phase(s) within a cycle.

Effect of Level of Compensation.
Most of the schemes which have been reported in the literature are basically designed for a specific compensation level; as the compensation level increases or decreases, the performance of schemes may get affected, and also at higher compensation levels, the SSR (subsynchronous resonance) phenomenon is predominant.To know the feasibility of the proposed scheme with the wide variations in the level of compensation level (from %Xc � 10%-80%), various simulation studies have been performed.Table 9 summarizes the results of the simulation studies.e results approve the accurate effectiveness of the proposed technique under wide variations in the compensation level.
e proposed scheme gives a good result for the classification of faults and faulty phase(s).

Effect of Change in System
Frequency.In the literature survey, we found that authors have not been discussed the performance of their schemes under wide variations in  Modelling and Simulation in Engineering system frequency.System frequency matters a lot in the protection of an electrical power system network.Various power system components such as induction machine, transformers, generators, and their operations depend on the frequency of the electrical system.Also, the stability of the power system relies on the frequency of the system.If    Modelling and Simulation in Engineering frequency deviation between the source end and the load end is more, then there is a probability of generators falling out of synchronism.To test the feasibility of the proposed method for the change in system frequency, consider fault type is DLGF in phases A and B with FR of 20 Ω and FIA of 0 °at 170 km from relaying point B4 with wide variations in system frequency.Results are illustrated in Table 10.
Consider fault type is a double line-to-ground fault in phases A and B with an FR of 20 Ω and FIA of 0 °at 170 km from relaying bus B4. e behaviour of voltage, current, and the proposed scheme during the ABG fault is shown in Figure 10.
Figure 10(c) shows that the outputs of the fault classification network wherein phases A and B and ground G become high after 4.2 ms, 3.5 ms, and 6.4 ms respectively,   and phase C is low all the time.Results approve the accurate performance of the proposed method under wide variations in system frequency.
e proposed scheme gives a good result for the classi cation of fault and faulty phase(s) within 7 ms.

E ect of Heavy Load Interconnection.
Performance of the presented CDFTF-based technique has also been investigated for heavy load condition.Nature of the load is probabilistic in the distribution side.Sometimes, the relay considers sudden change in the load on bus as a fault.e relay may mal-operate, and the healthy part of the system might be removed, which creates nonreliability of power and causes revenue losses.In order to investigate the e ect of heavy load interconnection on the e ectiveness of the proposed scheme, a variety of simulations has been carried out, considering wide variations in system frequency.Some of the simulation results are presented in Table 11.Modelling and Simulation in Engineering Consider the load of P 1000 MW and Q 800 MVAr is inserted on bus B2 in Figure 1, and the switching instant of load to bus B2 is 0.5 sec at the system frequency of 60 Hz.Fault classi cation outputs during this heavy load interconnection are shown in Figures 11(a A, B, and C, and ground G is low (0) all the time.e results approve that performance of the proposed scheme is perfect with varying system frequency.

Validation of the Proposed Scheme
Using EMTDC/PSCAD In order to test the proposed CDFTF-based scheme with more realistic system conditions, di erent fault situations have been simulated in the modi ed WSCC 3-machine 9bus system [26] using EMTDC/PSCAD software.e system parameters are given in Appendix B. e single-line diagram of the modi ed WSCC 9-bus system is shown in Figure 12. e relay is placed near to bus 7, so the transmission line  ( e fault classification modules correctly identify the involvement of phase(s) and ground.For instance, CA fault is created at 160 km, FIA � 90 °, FR � 0.001 Ω, and % Xc � 40%; in this case, the three-phase voltage and current signals obtained from PSCAD software simulation are shown in Figures 13(a) and 13(b), and output of the fuzzy fault classifier is shown in Figure 13(c).Figure 13(c) shows the performance of the classification module in which phases A and C rise up (1) both at 3 ms and 5 ms, respectively, while phase B and ground G remain low (0) after the inception of the fault at 2.005 sec.Some of the test results are presented in Table 12.Analyzing the results of Table 12, it is concluded that the proposed method has an accurate and reliable performance in various system conditions in the modified WSCC 3-machine 9-bus system.
For investigating the robustness of the proposed scheme, different faults are simulated in different conditions by varying different fault parameters.Total fault cases simulated are 5 (RF value) × 32 (fault locations) × 8 (FIA) × 10 (fault type) + 20 � 12820 cases.All these test cases have been applied to the proposed scheme, and the fault classification accuracy and correctness are measured in terms of the confusion matrix and presented in Table 13.e confusion matrix is a very concrete method to measure of robustness and accuracy of the proposed scheme.It can be observed from the confusion matrix that all the cases are predicted by the proposed scheme with an average accuracy of 99.678%.e result confirms that the proposed CDFTF-based scheme works correctly for the EMTDC/PSCAD fault simulation also.Modelling and Simulation in Engineering

Comparisons with Other Schemes
A summarized result of the comparative performance evaluation of the proposed CDFTF-based scheme with some other classification methods available in the literature is shown in Table 14.Most of the schemes reported in Table 14 have not discussed regarding the evolving fault, change in the system frequency, and heavy load interconnection.In most of the cases, the proposed schemes take half cycle time to classify the faults and the accuracy is about 100% compared to all other methods shown in Table 14.It can be observed that the time required by the proposed CDFTF-based scheme to classify the fault is 1/2-1 cycle.In addition, the proposed scheme is robust to wide variations in fault parameters, and moreover the scheme works well for evolving fault classification also.Furthermore, the performance is not affected by change in frequency and heavy load interconnection which have not been considered by earlier reported techniques.

Conclusion
is article presents a combined discrete Fourier transform and fuzzy logic based relaying scheme for protection of the series compensated transmission line.e process is started at retrieving the current and voltage signal features and preprocessing through discrete Fourier transform to obtain the fundamental component of voltage and current.e voltage and current features are used to build the fuzzy rule base for detection and classification of faults.e speed of the presented relaying technique is within half cycle of power frequency.Regarding fault detection and classification, the algorithm is capable of detecting and classifying all types of faults under varying fault and system conditions.Also, the variation in fault location, fault resistance, system frequency, and evolving fault do not affect the classification process.e CDFTF-based fault classification scheme has proved to be reliable, fast, and accurate against different fault situations in different series compensated transmission systems.System data for WSCC 3-machine 9-bus configuration: Generator

Figure 1 :
Figure 1: Single-line diagram of a series compensated power system network.
) and 4(b) show the time domain signals of 3phase voltage and current during the AB fault occurred at 135 km from the relaying point with FR � 10 Ω, FIA � 0 °at 0.5 sec.Figure4(c)shows the performance of the classification module in which phases A and B rise up (1) both at 0.5042 sec.Phase C and ground G remain low (0) after the inception of the fault at 0.5 sec.So, the proposed scheme provides better protection, covering 90% of the line length.
) and5(b)  show the input to FFC 3-phase time domain voltage and current signals.Figure5(c) presents the performance of FFC output.In Figure5, LLG (ABG)-type fault occurred in protected SCTS with FR � 40 Ω and FIA � 45 °at FL � 205 km is shown.e output of FFC shows that phases A and B and ground G go high (1) at 0.5067 sec, 0.5108 sec, and 0.5083 sec, respectively, after the inception of the fault at 0.5025 sec with phase C remaining low (0) and unchanged, confirming the nature of ABG fault.Table classification inputs and outputs during ABC-type LLL fault including FIA � 180 °at 175 km from the relaying point are shown in Figure6.3-phase sinusoidal voltages and currents are shown in Figures6(a) and 6(b), respectively.Figure6(c)shows the outputs of FFC where all the three faulty phases A, B, and C become high (1) after 0.5167 sec and ground output G remains low (0) all the time.
) and 8(b) present the three-phase time domain voltage and current signal, and the output of FFC is presented in Figure8(c).Single line to ground (BG) has been considered initially with FR of 15 Ω and fault inception time being 0.51 sec at 90 km from relaying bus B4. is BG fault is transformed into double line-to-ground fault (BCG) with FR

e 3 -
phase voltage and current signals are shown in Figures 9(a) and 9(b) for a DLGF (double line-to-ground

Table 1 :
Fuzzy rule base for fuzzy-based faulty phase classification.
Modelling and Simulation in Engineering 4.2.Effect of Fault Resistance.Another parameter that might have an impact on fault classification is fault resistance because, in the case of faults involving ground, FR may cause incorrect operation of the conventional distance relay.eimpacts of this parameter on the proposed scheme have been studied with variations in fault resistance.Test results during variations of FR on the presented CDFTF-based technique are shown in Table5.e proposed method has been proved to be effective in classifying the fault type with variations in fault resistance ranging from 0.001 Ω to 100 Ω. Figures5(a

Table 3 :
Faulty phase detection and fault classification using FFC with variations in fault parameters.

Table 8 :
Simulation results for evolving faults.
FT1, initial fault types; FT2, secondary fault types; FR1, initial fault resistance; FR2, secondary fault resistance; IT1, inception time for the initial fault type; IT2, inception time for the secondary fault type.

Table 10 :
Simulation results for the wide variations in system frequencies (FIA 0 °and FL 170 km).

Table 11 :
Simulation results for the heavy load interconnection (FIA 0 °and FL 165 km).

Table 13 :
Confusion matrix for the CDFTF-based scheme.

Table 12 :
Effect of fault resistance, fault inception angle, and fault location.

Table 14 :
Comparisons with other schemes.