Selection of Optimal Mother Wavelet for Transmission Line Protection

Selection of Optimal Mother Wavelet for Transmission Line Protection

P. Balakrishnan

Professor, Department of Electrical Engineering, Annasaheb Dange College of Engineering & Technology, Ashta, Sangli, Mahrastra

Abstract The current and voltage signals of the system experience transients when faults in transmission lines occur. Wavelet analysis can be used to analyse these transients in order to locate, classify, and detect faults. In this study, travelling wave theory is used to locate the line's flaw. In order to determine the best mother wavelet for transmission line protection, this study also compares four distinct mother wavelets, including the Daubechies, Haar, Symlet, and biorthogonal wavelets. The outcome suggests that the suggested method is very straightforward, quickly detects defects, and is also able to classify faults and properly pinpoint the fault's location.

Index TermsBiorthogonal wavelet, Daubechies wavelet, Maximum norm value, Mother wavelet, Travelling wave theory, Threshold detail coefficient.

1. INTRODUCTION

   An electric power system comprises of three components, namely generation, transmission and distribution. Among these components, transmission line protection is an important task in safeguarding the power system. To deliver electricity to the users, these transmission lines cover hundreds of kilometers. Due to their exposure to the environment, there is a very high likelihood that a transmission line accident may develop. In an electric power system, the fault is any abnormal flow of electric current. Unbalanced and balanced faults are the two basic categories for transmission line faults.

   The most prevalent of these faults, single-phase to ground problems, are caused by lightning strikes, tree collisions with power lines, mechanical failure of the insulator string due to fog, salt spray, and snow loading, and lightning strikes. The three-phase fault is most severe whereas single phase to ground fault is least severe. Faults may also occur due to natural reasons which are beyond the control of mankind. Various methods have been employed for fault detection and classification. Few of the techniques are Wavelet Transform [1], Fuzzy Logic [2], Artificial Neural Network (ANN)[3], Support Vector Machines (SVM) [4], [5]. Combined techniques have already been used, such as WT with ANN [6], [7], WT with Fuzzy [8]. Though the popularity of ANN, it has been widely criticized because it requires a considerable amount of training [9]. Techniques such ANN, and Fuzzy logic are dependent on training for knowledge representation based on a large sample, leading to large computational time [10].

   K. Sathiyasekar

   Professor, Department of ECE, Prathyusha Engineering College, Tiruvallur, Chennai

   The wavelet transforms based approaches have been quite successful in detection of fault with classification due to its ability to express a faulted signal both in time and frequency. The Continuous Wavelet Transform (CWT) is more complicated to implement because the information of interest is frequently a combination of features that are well localised temporally or spatially, and the CWT is calculated by varying the size of the analysis window, moving the window in time, and multiplying the signal.

   This necessitates the employment of analytical techniques that are sufficiently flexible to handle signals in terms of their localization in time and frequency [11]. Proposed a transmission line protection using the DWT, [12] Describes that DWT based technique is an excellent online tool for relaying applications. [13], Selecting the optimum mother wavelet is the one main challenge in using wavelet transform, if different mother wavelets are applied to the matching signal, it may produce different results. According to [14], detecting power system transients was equally effective using the db4, coiflet, and b-spline.

   The type of fault, the grounding resistance, the load circumstances, and system running away are all factors that are taken into consideration by existing methods for fault location, such as detecting changes in impedance or voltage and current of the line before and after a problem occurred. This paper represents the location of the fault method based on travelling wave theory. If a fault on line occurs, an unexpected change in voltage or in current at the fault point produces a high-frequency signal called a travelling wave [15].

   This travelling wave moves away from the fault location along the line in both directions. Using the difference in the arrival times of a fault wave at two ends of a faulted line, the travelling wave fault location method can be used to determine the location of a fault. Although each study enhances the ability to identify, classify, and locate transmission line faults to some level, they all have disadvantages as well.

   This paper evaluates four different mother wavelets: Daubechies (db6 & db4), Symlet 5, Bior 5.5 and Haar (db1) families in order to choose the most appropriate wavelet for fault detection, classification and location purpose. Decomposition on a single level is used because it contains the most information compared to decomposition on levels 2, 3, and so on. The more levels you go up, the more

   information you lose because each level's frequency component is halved. Computational time is decreased by using single level decomposition.

2. WAVELET TRANSFORM

   A novel mathematical method called the Wavelet

   below equation (1),

   Nw 2

   Ew [dw (k)]

   k 1

   (1)

   transform was created in 1980. Power system protection and

   Where, dw k

   is the wavelet coefficient of

   wth window

   power quality analysis are the two main applications of

   WT[16]. Excellent characteristics of wavelet

   and

   N w may be the window length which is calculated

   transformations include their ability to create small waves that have finite energy and integrate to zero. Wavelet transform offers numerous basis functions that can be

   as, Nw Ns

   number.

   2 , here

   Ns may be the samples of any

   employed as the mother wavelet as opposed to Fourier analysis, which depends on a single basis function. The short time Fourier transform utilises a single fixed window, whereas the wavelet transform uses short windows at high frequencies and long windows at low frequencies. This is the main distinction between the two transforms.By using wavelet transform, non stationary signals, i.e., whose frequency response varies with time can be analysed, whereas Fourier transform is not suitable. Signals can be analysed using the wavelet transform concurrently in the time and frequency domains. There are several different mother wavelet types available for use in wavelet analysis. When multiple Mother wavelets are used to analyse the same signal, the outcomes will vary. Mother wavelets typically exhibit characteristics including orthogonality, compact support, symmetry, and vanishing moment. Properties of the mother wavelet are taken into account while choosing a mother wavelet based on earlier studies. However, it's common to find many mother wavelets with the same characteristics. To get around this, when choosing a mother wavelet, the similarity between the signal and the mother wavelet is taken into account. Discrete Wavelet Transform (DWT) and Continuous Wavelet Transform (CWT) are the two types of wavelet transform (DWT).

   1. Discrete Wavelet Transform:

   The DWT was founded in 1976 by Croiser, Esteben, and

3. DESCRIPTION OF PROPOSED TRANSMISSION LINEFAULT ANALYSIS METHOD

   The simulink's power block set was used to build a simulation model that generates the transient signals of three-phase current. To find, categorise, and identify the defect, a discrete wavelet transformation is used with single level decomposition for three-phase current signals.

   1. Fault Detection Module

      Three basic steps make up the application of the suggested method. The fault is first identified, then the fault is classified, and the fault's location is finally determined. The three phase current signals of the transmission line used in this suggested system are accepted as input, decomposed using the discrete wavelet transform, and compressed using the remove near zero approach to provide the maximum norm value and threshold detail coefficient values. The maximum norm value is used for fault detection and threshold detail coefficient is used for classification purposes. In this paper, different mother wavelet such as d6, db4, haar (db1), sym 5, bior 5.5 is used in order to select the optimal wavelet for transmission line protection. Maximum norm values are calculated for all different types of fault using the wavelet tool box. The highest acceptable standard value for a normal state is used as a benchmark when comparing it to an aberrant one. A problem is identified if the signal's maximum norm value exceeds the value for a

      Galand, who created a method for breaking down discrete

      time signals [3]. In DWT, a digital filtering technique is used to generate a time-scale representation of a discrete signal. The signal that has to be analysed is run through a

      normal state. The norm of detail coefficient d1

      calculated as,

      nd 1

      d1 [ d (k)] 2

      can be

      (2)

      unique filter with a unique cutoff frequency at various

      scales. The discrete time-domain signal is successively low-pass and high-pass filtered before being used to calculate the DWT. In single level decomposition, the signal is decomposed as D1 and A1, with the frequency band of

      k 1 1

      Where nd may be the No. of detail coefficient.

   2. Fault Classification Module

      For fault classification purpose, the threshold detail

      fs 2 fs 4 ,

      0 f s

      4 . In the second level decomposition,

      coefficient values are considered. A phase's threshold value

      the low pass filter, A1 is split into D2 and A2 as the

      will be higher than its typical condition value in the event of

      frequency band D2 is

      fs 4 fs 8

      and A2 is

      0 fs 8 .

      a single phase to ground (A-G) fault, but the other two

      The wavelet coefficient energy can be calculated as shown

      phases are unaffected (remains same). When there is a

      double phase (AB) fault, the threshold values for phases A

      and B will be equal but higher than they would be under normal circumstances. Phases A and B's threshold values will not be equal in value, but rather higher than those for a normal situation in the case of a double phase to ground fault (AB-G) scenario. A threshold value for each phase will be greater than the value for each phase's normal state in the case of a three phase fault (ABC).

   3. Fault Location module

   The algorithm for fault location is performed after the completion of fault detection and classification process. In this process, different fault current signal are taken which are obtained from a simulated power system model, and it is transformed into the modal signal using Clarke modal transformation. Then these modal signals are decomposed using DWT with different mother wavelet such as d6, db4, haar (db1), sym 5, bior 5.5 in order to choose the ideal wavelet. After the decomposition, the peak magnitude of current signal at the lowest scale of the detail coefficient is used to determine the location of the fault. The location of fault is calculated by formula,

   Fig. 1. Simulated Power System Model.

   The corresponding Thevenin sources on either side of the line are estimated to have a short circuit capacity of 1.25 GVA and an X/R ratio of 10. Table 1 displays the transmission line parameters for the test system.

   TABLE I

   x v(ta tb )2

   (3)

   TEST SYSTEM TRANSMISSION LINE PARAMETERS

   Positive sequence resistance R1, /km	0.018
   Zero sequence resistance R0, /km	0.218
   Positive sequence Inductance L1, H/km	0.000929
   Zero sequence Inductance L0, H/km	0.00328
   Positive sequence Capacitance C1, F/km	1.2571e-008
   Zero sequence Capacitance C0, F/km	7.8555e-009

   Where ta and tb are corresponding to the time at which the modal signal wavelet coefficient at lowest scale, show their

   peak values. If the spread value of the signal is identified, then the gap of the fault is easily found. Wave propagation speed is influenced by line parameter values like inductance

   (L) and capacitance (C). Where of propagation.

   v 1

   LC is the velocity

   B. Performance of the Programmed Fault Signals

4. RESULTS AND DISCUSSIONS

   The suggested algorithm has been tested for all types of Single Phase to Ground Faults, but only Phase A to Ground is shown here. It has also been tested for all types of Double Phase Faults, with or without ground, but only Double Phase AB and Double Phase AB-G are shown here.

   A. Description of Line Diagram of Test System

   The system under study consists of a 220 KV transmission circuit with sections measuring 200 km for section 1, 120 km for section 2, and 110 km for section 3. These sections are connected to sources at both ends. The power system model developed in power system is given in Fig. 1.

   1. Normal Condition

      Fig. 2 displays the three-phase current signal under ideal conditions. Here, using DWT and various mother wavelet types, including db6, db4, haar (db1), sym 5, and bior 5.5, the maximum norm value and threshold detail coefficient values are determined for this circumstance. Maximum norm and threshold detail coefficient of three phases at normal condition using db6, db4, haar (db1), sym 5, bior 5.5 wavelet are shown in Table 2, 3, 4, 5 & 6. These calculated values are taken as reference for further detection and classification purposes.

      Fig. 2. Simulated Result for Normal Condition.

      TABLE II

      MAXIMUM NORM AND THRESHOLD DETAIL COEFFICIENT OF THREE PHASE AT NORMAL CONDITION USING DB6 WAVELET.

      Parameter	Phase A	Phase B	Phase C
      Max Norm	0.0102	0.0844	0.0741
      Threshold	0.0134	0.1109	0.0974

      TABLE III

      Parameter	Phase A	Phase B	Phase C
      Max Norm	0.0135	0.0985	0.0849
      Threshold	0.0225	0.1643	0.1417

      MAXIMUM NORM AND THRESHOLD DETAIL COEFFICIENT OF THREE PHASE AT NORMAL CONDITION USING DB4

      TABLE IV

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT NORMAL CONDITION USING HAAR.

      Parameter	Phase A	Phase B	Phase C
      Max Norm	0.2458	0.1719	0.1724
      Threshold	0.1738	0.2432	0.2439

      TABLE V

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT NORMAL CONDITION USING SYMLET 5.

      Fig. 3. Simulated Result for Phase A to Ground Fault

      TABLE VII

      MAXIMUM NORM AND THRESHOLD DETAIL COEFFICIENT OF THREE PHASE AT SINGLE PHASE TO GROUND FAULT USING DB6 WAVELET.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase A-G	Max Norm	0.2941	0.0844	0.0741
      	Threshold	0.3073	0.1109	0.0974
      Phase B-G	Max Norm	0.0102	0.2683	0.0741
      	Threshold	0.0134	0.3047	0.0974
      Phase C-G	Max Norm	0.0102	0.0844	0.3142
      	Threshold	0.0134	0.1109	0.3095

      TABLE VIII

      MAXIMUM NORM AND THRESHOLD DETAIL COEFFICIENT OF THREE PHASES AT SINGLE PHASE TO GROUND FAULT USING DB4.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase A-G	Max Norm	0.2902	0.0988	0.0846
      	Threshold	0.3100	0.1648	0.1412
      Phase B-G	Max Norm	0.0145	0.2245	0.0860
      	Threshold	0.0243	0.2903	0.1435
      Phase C-G	Max Norm	0.0130	0.0989	0.2707
      	Threshold	0.0218	0.1651	0.3122

      TABLE IX

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT SINGLE PHASE TO GROUND FAULT USING HAAR.

      Parameter	Phase A	Phase B	Phase C
      Max Norm	0.0118	0.0978	0.0859
      Threshold	0.0164	0.1354	0.1190

   2. Single Phase to Ground

      The three current signals of phase A to Ground fault are given in Fig. 3. Maximum norm and threshold detail coefficient of 3 phases of single phase to ground fault condition using db6, db4, haar (db1), sym 5, bior 5.5 wavelet are shown in Tables 7, 8, 9, 10, 11. Each phase maximum norm value and threshold detail coefficient value of A-G fault is compared with the normal condition value.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase A-G	Max Norm	0.2198	0.1722	0.1707
      	Threshold	0.3108	0.2435	0.2414
      Phase B-G	Max Norm	0.1710	0.2128	0.1710
      	Threshold	0.2418	0.3010	0.2419
      Phase C-G	Max Norm	0.1715	0.1707	0.2203
      	Threshold	0.2426	0.2414	0.3115

      TABLE X

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT SINGLE PHASE TO GROUND FAULT USING SYMLET 5.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase A-G	Max Norm	0.2333	0.0978	0.0859
      	Threshold	0.3061	0.1354	0.1190
      Phase B-G	Max norm	0.0118	0.2552	0.0859
      	Threshold	0.0164	0.2963	0.1190
      Phase C-G	Max Norm	0.0118	0.0978	0.2688
      	Threshold	0.0164	0.1354	0.3105

      TABLE XI

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT SINGLE PHASE TO GROUND USING BIOR 5.5

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase A-G	Max Norm	0.2329	0.0794	0.0691
      	Threshold	0.3091	0.0973	0.0847

      Phase B-G	Max Norm	0.0117	0.2459	0.0691
      	Threshold	0.0143	0.2986	0.0847
      Phase C-G	Max Norm	0.0105	0.0795	0.2403
      	Threshold	0.0128	0.0975	0.3124

      TABLE XIII

      MAXIMUM NORM AND THRESHOLD DETAIL COEFFICIENT OF THREE PHASES AT DOUBLE PHASE FAULT USING DB4.

      If the maximum norm value exceeds a usual situation value means, a fault is noticed. From the below tables it is clear that under the A-G Fault condition, maximum norm value of phase A is greater than the normal condition value, so it is detected as phase A is faulted. Similarly, a threshold value of phase A is greater than the normal condition value of phase A and the other two phase values are equal to the normal condition values. This indicates that phase A to Ground fault is detected.

   3. Double Phase Fault

      The three-phase current of phase A-B fault are shown in Fig. 4.

      Fig. 4. Simulated Result for Phase A to B Fault.

      Maximum norm and threshold detail coefficient of three phases of double phase fault condition using db6, db4, haar (db1), sym 5, bior 5.5 wavelet are shown in Table 12,13,14, 15,16. Maximum norm value and threshold values of each phase under AB fault are compared with normal condition values. From the below tables it is clear that the maximum norm value of A and B phase is greater than normal situation values of phase A and B, this indicates that phase A and B is affected. Similarly, a threshold value of phase A and B are same in value, but greater than the normal condition value of phase A and B. This indicates that phase AB is not connected to Ground.

      TABLE XII

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase AB	Max Norm	0.3509	0.3059	0.0741
      	Threshold	0.3167	0.3167	0.0974
      Phase BC	Max Norm	0.0102	0.3046	0.3046
      	Threshold	0.0134	0.3157	0.3157
      Phase AC	Max Norm	0.2876	0.0844	0.2876
      	Threshold	0.3179	0.1109	0.3179

      MAXIMUM NORM AND THRESHOLD DETAIL COEFFICIENT OF THREE PHASE AT DOUBLE PHASE FAULT USING DB6 WAVELET.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase AB	Max Norm	0.2289	0.2289	0.0849
      	Threshold	0.3119	0.3119	0.1417
      Phase BC	Max Norm	0.0135	0.2848	0.2848
      	Threshold	0.0225	0.3147	0.3117
      Phase AC	Max Norm	0.2608	0.0985	0.2608
      	Threshold	0.3195	0.1643	0.3156

      TABLE XIV

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT DOUBLE PHASE FAULT USING HAAR.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase AB	Max Norm	0.2212	0.2202	0.1706
      	Threshold	0.3128	0.3114	0.2441
      Phase BC	Max Norm	0.1738	0.2230	0.2224
      	Threshold	0.2458	0.3154	0.3145
      Phase AC	Max Norm	0.2257	0.1719	0.2238
      	Threshold	0.3191	0.2432	0.3166

      TABLE XV

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT DOUBLE PHASE FAULT USING SYMLET 5.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase AB	Max Norm	0.2561	0.2561	0.0859
      	Threshold	0.3197	0.3034	0.1190
      Phase BC	Max Norm	0.0118	0.2729	0.2729
      	Threshold	0.0164	0.3157	0.3146
      Phase AC	Max Norm	0.2288	0.0978	0.2288
      	Threshold	0.3233	0.1354	0.3233

      TABLE XVI

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT DOUBLE PHASE USING BIOR 5.5

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase AB	Max Norm	0.2480	0.2480	0.0691
      	Threshold	0.3104	0.3104	0.0847
      Phase BC	Max Norm	0.0108	0.2314	0.2314
      	Threshold	0.0133	0.3144	0.3144
      Phase AC	Max Norm	0.2458	0.0792	0.2458
      	Threshold	0.3207	0.0970	0.3162

   4. Double Phase to Ground

      The three phase current signals of phase AB to Ground fault are shown in Fig. 5.

      Fig. 5. Simulated Result for Phase AB to Ground Fault.

      Maximum norm and threshold detail coefficient of three phases at phase AB to ground fault condition using db6, db4, haar (db1), sym 5, bior 5.5 wavelet are shown in Table 17, Table 18, Table 19, Table 20, Table 21. Maximum norm value and threshold values of each phase under AB to Ground fault are compared with normal condition values. From the below tables it is clear that the maximum norm value of phases A and B is greater than normal condition values of phase A and B, this indicates that phase A and B is affected.

      TABLE XVII

      MAXIMUM NORM AND THRESHOLD DETAIL COEFFICIENT OF THREE PHASE AT DOUBLE PHASE TO GROUND FAULT USING DB6 WAVELET.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase AB-G	Max Norm	0.2683	0.2942	0.0741
      	Threshold	0.3190	0.3109	0.0974
      Phase BC-G	Max Norm	0.0102	0.3137	0.2688
      	Threshold	0.0134	0.3127	0.3133
      Phase AC-G	Max Norm	0.2932	0.0842	0.2438
      	Threshold	0.3140	0.1109	0.3146

      Similarly, a threshold value of phase A and B are greater than the normal condition value of phase A and B but the values of phase A and phase B are different. This indicates that phase AB is connected to ground.

      TABLE XVIII

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT DOUBLE PHASE TO GROUND FAULT USING DB4.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase AB-G	Max Norm	0.2445	0.2600	0.0864
      	Threshold	0.3190	0.3163	0.1442
      Phase BC-G	Max Norm	0.0139	0.2698	0.3197
      	Threshold	0.0232	0.3132	0.3149
      Phase AC-G	Max Norm	0.2753	0.0997	0.2785
      	Threshold	0.3164	0.1663	0.3147

      TABLE XIX

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT DOUBLE PHASE TO GROUND FAULT USING HAAR.

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase AB-G	Max Norm	0.2257	0.2239	0.1580
      	Threshold	0.3192	0.3167	0.2234
      Phase BC-G	Max Norm	0.1592	0.2235	0.2236
      	Threshold	0.2251	0.3161	0.3162
      Phase AC-G	Max Norm	0.2230	0.1592	0.2242
      	Threshold	0.3154	0.2252	0.3170

      TABLE XX

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT DOUBLE PHASE TO GROUND FAULT USING SYMLET 5.

      Fault Type	Parameter	Phase	Phase B	Phase C
      Phase AB-G	Max Norm	0.2535	0.2478	0.0859
      	Threshold	0.3187	0.3178	0.1190
      Phase BC-G	Max Norm	0.0118	0.2756	0.2447
      	Threshold	0.0164	0.3140	0.3165
      Phase AC-G	Max Norm	0.2914	0.0978	0.2523
      	Threshold	0.3126	0.1254	0.3203

      TABLE XXI

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT DOUBLE PHASE TO GROUND FAULT USING BIOR 5.5

      Fault Type	Parameter	Phase A	Phase B	Phase C
      Phase AB-G	Max Norm	0.2408	0.2561	0.0694
      	Threshold	0.3180	0.3161	0.0851
      Phase BC-G	Max Norm	0.1119	0.2347	0.2327
      	Threshold	0.0137	0.3215	0.3152
      Phase AC-G	Max Norm	0.2291	0.0801	0.2559
      	Threshold	0.3183	0.0982	0.3195

   5. Three Phase Fault

      The three phase current signals for this case is shown in Fig. 6.

      Fig. 6. Simulated Result for Three Phase Fault.

      Maximum norm and threshold detail coefficient of three phases at three phase fault condition using db6, db4, haar

      FAULT TYPE	Db6	Db4	Haar	Symlet 5	Bior 5.5
      A-G	83.032	83.051	83.050	83.034	83.033
      B-G	68.822	79.690	79.270	78.980	78.970
      C-G	69.780	80.345	80.150	79.120	80.342
      A-B	69.220	80.348	80.149	80.410	80.347
      B-C	70.615	80.627	80.021	80.703	80.586
      A-C	69.780	80.345	80.153	80.410	69.850
      AB-G	72.990	83.551	83.295	83.556	72.788
      BC-G	72.284	78.739	79.010	78.998	78.998
      AC-G	76.449	80.416	80.414	69.648	80.414
      ABC	69.782	80.344	80.413	80.414	69.648

      (db1), sym 5, bior 5.5 wavelet are shown in Table 22, Table 23, Table 24, Table 25, Table 26.

      TABLE XXII

      MAXIMUM NORM AND THRESHOLD DETAIL COEFFICIENT OF THREE PHASE AT THREE PHASE FAULT USING DB6 WAVELET.

      Parameter	Phase A	Phase B	Phase C
      Max Norm	0.2711	0.2400	0.3070
      Threshold	0.3134	0.2994	0.3230

      TABLE XXIII

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT THREE PHASE FAULT USING DB4.

      Parameter	Phase A	Phase B	Phase C
      Max Norm	0.2642	0.2220	0.2555
      Threshold	0.3176	0.3054	0.3188

      TABLE XXIV

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT THREE PHASE FAULT USING HAAR.

      Parameter	Phase A	Phase B	Phase C
      Max Norm	0.2245	0.2198	0.2236
      Threshold	0.3175	0.3108	0.3162

      TABLE XXV

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT THREE PHASE FAULT USING SYMLET 5.

      Parameter	Phase A	Phase B	Phase C
      Max Norm	0.2365	0.2234	0.2339
      Threshold	0.3246	0.3001	0.3154

      TABLE XXVI

      MAXIMUM NORM AND THRESHOLD DETAILS OF THREE PHASE AT THREE PHASE FAULT USING BIOR 5.5

      Parameter	Phase A	Phase B	Phase C
      Max Norm	0.2447	0.2428	0.2633
      Threshold	0.3140	0.3083	0.3130

      From the below tables it is clear that the maximum norm value of all the three phases (ABC) is greater than normal condition values of all the three phases. Similarly, a threshold value of all the three phases is greater than normal condition values.

   6. Fault Location results

   The fault location is found for all different fault types using different mother wavelet such as d6, db4, haar (db1), sym 5, bior 5.5. The different mother wavelet is used in order to select the optimal wavelet. The location for each fault is calculated using the equation (3) and the results are shown in Table 27.

   B. COMPARISON PERFORMANCES OF DB6 WITH OTHER WAVELETS.

   In this paper, different mother wavelet such as db6, db4, haar (db1), sym 5, bior 5.5 is used for transmission line fault protection. In fault classification, it is difficult to distinguish the double phase fault from double phase to ground fault condition while using db4, haar (db1), sym 5, bior 5.5 as a mother wavelet, whereas db6 wavelet gives a very accurate classification.

   Fig. 7. Accuracy of fault classification using different Mother wavelets

   The accuracy of fault classification using different mother wavelets is shown in Fig. 7. At fault location, the db6 as mother wavelet provide better accuracy than other wavelet such as db4, haar (db1), sym 5, bior 5.5. The accuracy of fault location is shown in Fig. 8. Overall db6 as a mother wavelet provides good accuracy in transmission line protection.

   TABLE XXVII

   FAULT LOCATION ON BUS 1 WITH RESPECT TO 2 IN Km

   Fig. 8. Accuracy of fault location using different mother wavelet

5. CONCLUSION

The suggested system's Simulink model has been created, and fault analysis has been done using the Discrete Wavelet Transform with wavelets like db6, db4, haar (db1), sym 5, and bior 5.5. Maximum Norm and Threshold values, which are utilised for Fault Detection and Classification, are computed from DWT. By calculating the travelling-wave propagation periods, the fault location is identified. Among these wavelets, db6 is determined to be the most effective for transmission line protection, followed by db4, haar (db1), sym 5, and bior 5.5. Using db4, haar (db1), sym 5, and bior

5.5 wavelets for fault classification, it is challenging to discern between a double phase fault and a double phase to ground fault. For transmission line protection, the db6 mother wavelet is therefore the best option. The outcome demonstrates that the suggested system can accurately locate the issue, identify the fault type, and detect faults quickly.

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[10] Zhengyou He, Ling Fu, Sheng Lin, and Zhiqian Bo, Fault detection and classification in EHV transmission line based on wavelet singular entropy, IEEE Trans. Power Del., vol. 25, no. 4, pp. 2156-2163, Oct. 2010.

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