Line to Ground and Line to Line Fault Analysis in IEEE Standard 9 Bus System

Line to Ground and Line to Line Fault Analysis in IEEE Standard 9 Bus System

Sagnik Datta Aveek Chattopadhyaya Surajit Chattopadhyay Arabinda Das 

Electrical Engineering Department, Supreme Knowledge Foundation Group of Institutions, Mankundu, India

Electrical Engineering Department, GKCIET, Malda, India

Electrical Engineering Department, Jadavpur University, Jadavpur, India

Page: 
10-18
|
DOI: 
https://doi.org/10.18280/mmc_a.931-402
Received: 
14 August 2020
|
Accepted: 
5 December 2020
|
Published: 
31 December 2020
| Citation

OPEN ACCESS

Abstract: 

Line to Ground (LG) and Line to Line (LL) faults are the two most frequently encountered faults in any power system network. For the purpose of designing advanced protection systems, detection of the location as well as the identification of the type of fault, from a remote location is of paramount importance. In this paper a Discrete Wavelet Transform based statistical analysis has been carried out to detect the fault type and location of LG and LL faults. IEEE standard 9 bus system has been considered for this purpose. Faults are made to occur in the load buses and outgoing currents from the generator buses are analyzed by Discrete Wavelet Transform (DWT) as these current waveforms are non-stationary in nature. Statistical parameters are calculated from the approximate and detail coefficients which have been derived from the DWT. Based upon these parameters, a rule set has also been made. Simulation work is performed with the help of MATLAB. Methods proposed here can be helpful for designing better protection schemes.

Keywords: 

line to ground (LG) fault, line to line (LL) fault, digital signal processing, discrete wavelet transform (DWT), statistical analysis, skewness, kurtosis

1. Introduction

Electrical power system network consisting of several sources and loads helps in transfer of power from generating stations to consumers. Complexity in all the sectors of power system is increasing. Thus, for reliable operation of power system networks, proper identification of type and location of fault has become very much important. Two most frequently occurring faults in any power system network are line to ground (LG) and line to Line (LL) faults. A lot a research work is being carried out in the field of fault identification of power system networks. Elkalashy et al. [1] proposed a novel selectivity technique to detect the fault feeder in MV networks using the directionality of DWT detail coefficient of a residual current of each feeder. Wavelet transformation is used to analyze power system transients for identification of fault locations in double circuit transmission lines by Andanapalli et al. [2]. Dubeya et al. [3] proposed DWT and Independent component analysis (ICA) for detection of faulty negative sequence current in series compensated transmission line using Matlab or Simulink. Xie et al. [4] proposed a Wavelet transform based methods of measuring time and frequency information of high frequency transients produced by the faults on transmission lines for the purpose of locating the fault point. A relaying principle using Wavelet based artificial neural networks capable of classifying transients–including faults occurring on a protected line has been shown by Abdullah [5]. Devi et al. [6] has proposed a method of analysis of faults with different load conditions for localization, detection and classification of faults in transmission lines. Patel et al. proposed a novel technique or fault detection in high voltage transmission line using the wavelet transform during power swing condition [7, 8]. A method for identification of Line to Ground Fault in a standalone Wind Energy Conversion System using multi-resolution based DWT analysis has been proposed by Ray et al. [9]. Mishra et al. [10] proposed an improved method of transmission line fault classification using Wavelet Transform as well as impedance measurement and travelling wave theory. Chattopadhayay et al. [11] detected crawling of an induction motor by performing Wavelet decomposition of the stator current in Clarke Plane. Power Quality related different parameters have been assessed in Parke Plane by Chattopadhayay et al. [12]. Current Park Vector pattern approach is used for detection of electrical faults in an induction motor by S. Chattopadhyay et al. [13-15].

2. IEEE Standard 9 Bus System

Figure 1. IEEE standard 9 Bus system

Single line diagram of IEEE standard 9 bus system is shown below in Figure 1. The power system network consists of three generators, generator 1, 2 and 3 connected to bus 1, 2 and 3 respectively. It also has three load buses–Bus 5, 6 and 8.

Voltage and current rating of generator 1, 2 and 3 are 247.5 MW and 16.5 kV; 192 MVA and 18 kV; 126 MVA and 13.8 kV respectively. The rating of the load connected to bus 5, 6 and 7 are 125 MW and 50 MVAR; 90 MW and 30 MVAR; 100 MW and 35 MVAR respectively. Work presented here, attempts to identify type of fault as well as location of LG and LL fault DWT based statistical parameter analysis of the waveforms of outgoing currents from different generator buses in faulty conditions. The faults are made to occur at the load buses. However, the work may be extended to other type of faults taking place at other locations of the network also.

3. Fault Simulation

DWT based statistical parameter analysis of the outgoing currents from the generator buses   in healthy as well as faulty conditions have been performed to detect type of the fault and its location. LG and LL faults are made to occur in the load buses. Switching time of faults is set to 0.3-0.5 sec. The sampling frequency is taken to be 1000 Hz and total time of simulation is 0.8 sec. Very small total simulation time has been chosen to minimize the data size generated by the simulation software and computation time of the analysis process.

4. Results and Observation

DWT based decomposition of the generator bus outgoing currents are performed and approximate and detail coefficients and the process is carried out for both healthy and faulty conditions. Nine levels of decomposition of the current waveforms have been performed. After obtaining approximate and details coefficients in each level RMS, skewness and kurtosis values are computed. Hence, total six parameters are taken into account–skewness of approximate coefficient (Sa), skewness of detail coefficient (Sd), kurtosis of approximate coefficient (Ka), kurtosis of detail coefficient (Kd), RMS of approximate coefficient (RMSa) and RMS of detail coefficient (RMSd). In the entire DWT analysis, Daubechies4 (DB4) wavelet is considered as the mother wavelet. Each generator bus outgoing current is analyzed separately. Percentage deviation of all the above mentioned parameters are calculated from their corresponding healthy condition values are calculated using equation 1 shown below. So, in a healthy case the percentage deviations of the above mentioned parameters will be zero.

$\%$ Deviation $=\left|\frac{(\text { Healthy value })-(\text { Faulty value })}{\text { Healthy value }}\right| \times 100$     (1)

Results and the corresponding observations are presented below for all three generator buses one by one.

4.1 Observation from generator Bus 1

Percentage deviations of Sa, Sd, Ka, Kd, RMSa and RMSd are calculated and shown in Table A.1–A.6 (Appendix). Data given in the earlier mentioned tables have been presented in the form of graphs in Figures 2-4.

From Figure 2(a) it has been noticed that when LG fault occurs at Bus 5, percentage deviation of Sa at 6th level of decomposition is the greatest amongst all the parameters in all the levels. Figure 2(b) shows that for LL fault at Bus 5, greatest amount of percentage deviation occurs in RMSd at level 3.

Figure 2. Percentage deviation of different parameters of GEN Bus 1 for (a) LG fault at Bus 5 and (b) LL fault at Bus 5

Figure 3. Percentage Deviation of different parameters of GEN Bus 1 for (a) LG fault at Bus 6 and (b) LL fault at Bus 6

From Figure 3(a) shows that percentage deviation of RMSd at level 6 is the greatest when LG fault takes place at Bus 6. Figure 3(b) shows that for LL fault at Bus 6, percentage deviation of Sd at 7th level of decompositions becomes the greatest amongst all the parameters in all the levels.

Figure 4. Percentage deviation of different parameters of GEN Bus 1 for (a) LG fault at Bus 8 and (b) LL fault at Bus 8

From Figure 4 (a) shows that when LG fault occurs at Bus 8, percentage deviation of Kd at level 5 is the greatest amongst all the parameters. Figure 4(b) suggests that for LL fault at Bus 8, greatest amount of percentage deviation occurs in Sd at level 5.

4.2 Observation from generator Bus 2

Percentage deviations of RMS, skewness and kurtosis of approximate and detail coefficients are calculated and shown in Table A.7–A.12 (Appendix). Data given in these tables have been presented in the form of graphs in Figures 5-7.

From Figure 5(a) it has been seen that greatest amount of percentage deviation takes place in Sd at level 6 when LG fault occurs at Bus 5. Whereas, Figure 5(b) shows that RMSd has the greatest amount of percentage deviation at level 3 when LL fault takes place at Bus 5.

Figure 5. Percentage deviation of different parameters of GEN Bus 2 for (a) LG fault at Bus 5 and (b) LL fault at Bus 5

Figure 6. Percentage deviation of different parameters of GEN Bus 2 for (a) LG fault at Bus 6 and (b) LL fault at Bus 6

Figure 6(a) suggests that when LG fault takes place at bus 6, parameter Kd has the greatest amount of percentage deviation at level 5. Whereas, it has been observed from Figure 6(b) that for occurrence of LL fault at Bus 6, RMSd has the greatest amount of deviation at level 6.

Same procedure has been followed in case of LG and LL fault in Bus 8. In case of LG fault at Bus 8; Figure 7(a) given below, shows that the greatest amount of deviation is present in Kd at level 4. Figure 7(b) shown below suggests that for LL fault at Bus 8, Sa has the greatest amount of deviation is present in level 7.

Figure 7. Percentage deviation of different parameters of GEN Bus 2 for (a) LG fault at Bus 8 and (b) LL fault at Bus 8

4.3 Observation from generator Bus 3

Percentage deviations of RMS, skewness and kurtosis of approximate and detail coefficients are calculated and shown in Table A.13–A.18 (Appendix). Data given in these tables have been presented in the form of graphs in Figures 8-10.

From 8(a), it can be observed that greatest amount of deviation is present in parameter Sd at level 6, when LG fault occurs at Bus 5. Whereas, Figure 8(b) shows that for LL fault at Bus 8, the amount of percentage deviation is greatest in RMSd at level 3.

Same procedure is followed for LG and LL fault at bus 6 and the graphs are shown in Figure 9(a) and 9(b), which are presented below. From Figure 9(a) it has been seen that for occurrence of LG fault at Bus 6 greatest amount of percentage deviation is present in Kd at level 5. Whereas, Figure 9(b) shows that for LL fault at Bus 6, Sd has the greatest amount of deviation at level 5.

Figure 8. Percentage Deviation of different parameters of GEN Bus 3 for (a) LG fault at Bus 5 and (b) LL fault at Bus 5

Figure 9.

Graphical representations of the results for LG and LL faults at Bus 8 have been presented below in Figure 10(a) and 10(b).

Figure 10. Percentage deviation of different parameters of GEN Bus 3 for (a) LG fault at Bus 8 and (b) LL fault at Bus 8

From Figure 10(a) it has been observed that when LG fault occurs at Bus 8, percentage deviation of Kd at level 4 is the greatest. Whereas, the percentage deviation of Sa at level 6 is the greatest when LL fault takes place at Bus 8.

From the above discussion it can be observed that for a particular generator bus outgoing current, with the variation of type of fault and location of occurrence, parameter having the greatest amount of percentage deviation and the level at which it takes place changes. For a particular fault type and location one specific parameter possesses the greatest amount of deviation at a specific level of decomposition. Hence, by identifying the parameter and the level at which it has the greatest amount of deviation, location as well as the type of fault can be found out. It can also be seen that out of six parameters, four parameters turned out to be useful for fault analysis. These parameters are Sa, Sd, Kd, RMSd. Moreover, values of these parameters at five different levels–3, 4, 5, 6, 7 are used.

5. Rule Set

Based upon the observations made in the previous section a simple rule set has been prepared which can be used for discriminating the fault type and identifying the fault location by monitoring the outgoing current of any generator bus. It is presented in the Table 1 shown below.

Table 1. Rule set

Fault Type

Fault Location

Generator Bus used for observation

GEN Bus 1

GEN Bus 2

GEN Bus 3

Parameter with greatest

% deviation

Level

of occurrence

Parameter with greatest

% deviation

Level

of occurrence

Parameter with greatest

 % deviation

Level

of occurrence

LG

Bus 5

Sa

6

Sd

6

Sd

6

Bus 6

RMSd

6

Kd

5

Kd

5

Bus 8

Kd

5

Kd

4

Kd

4

LL

Bus 5

RMSd

3

RMSd

3

RMSd

3

Bus 6

Sd

7

RMSd

6

Sd

5

Bus 8

Sd

5

Sa

7

Sa

6

6. Case Studies and Validation

As real verification is practically impossible, the rule set presented in the previous section has been validated by simulating faults in IEEE standard 9 bus system. Three unknown cases are considered where the total time of simulation, fault duration time as well as the prefault condition of the loads have been varied. Results of the case studies have been given below in Table 2.

From Table 2 it has been observed that results in every case are very much optimistic.

Table 2. Details of the case studies

Sl.

No.

Known Facts

Observation from Bus

Parameter with greatest

% deviation

Level

of occurrence

Inference

Simulation

Details

Pre-fault Condition

1

Total simulation time 1 sec

and

fault duration

0.3–0.5 sec

Full load at Bus 5, 6 & 8

GEN Bus 1

Kd

5

LG at Bus 8

GEN Bus 2

Kd

4

GEN Bus 3

Kd

4

2

Total simulation time 1.2 sec

and

fault duration

0.4–0.7 sec

Full load at Bus 5, 6 & No load at Bus 8

GEN Bus 1

Sd

7

LL at Bus 6

GEN Bus 2

RMSd

6

GEN Bus 3

Sd

5

3

Total simulation time 1.5 sec

and

fault duration

0.6–0.9 sec

Full load at Bus 5, 8 & Half load at Bus 6

GEN Bus 1

RMSd

3

LL at Bus 5

GEN Bus 2

RMSd

3

GEN Bus 3

RMSd

3

7. Specific Outcome

The work presented here, shows a method of finding out fault type and location based upon a DWT based statistical parameter analysis of outgoing currents from the generator buses. Six different parameters are obtained for each generator bus outgoing currents in different conditions. Observation of the parameter having the greatest amount of percentage deviation from its corresponding healthy condition values and the level of occurrence reveals the type of fault and the location at which it takes place. A rule set has been prepared depending upon the observations and it has also been validated using three unknown cases where different simulation time, fault duration and load condition are used than that used for the analysis and preparation of the rule set. Results of the case studies have been found out to be very much satisfactory.

8. Conclusion

In the above work, LG and LL faults have been dealt with using DWT based statistical analysis of the outgoing currents from the generator buses and faults are considered at the load buses. Total six parameters are considered-skewness of approximate coefficient, skewness of detail coefficient, kurtosis of approximate coefficient, kurtosis of detail coefficient, RMS of approximate coefficient and RMS of detail coefficient. IEEE standard 9 bus system has been utilized for this purpose. Using the method proposed here, type and location of a fault can be found out by monitoring the outgoing currents from the generator buses. Present work only considers two types of faults and fault locations to be the load buses. However, this work can be extended for other type of faults occurring at locations other than load buses.

Appendix

Table A.1 Percentage deviation of different parameters of GEN Bus 1 outgoing currents for LG fault at Bus 5

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

99.999

15.211

13.993

19.774

5.2

15.726

2

133.999

66.766

13.993

76.494

5.2

109.051

3

589.999

92.979

13.993

81.534

5.2

2323.788

4

655.999

119.936

13.993

379.765

5.2

1021.738

5

999.815

2429.487

13.993

933.977

5.2

115.739

6

2999.999

2640.625

13.866

170.576

5.198

9.653

7

1820

828.333

14.241

32.614

5.24

4.663

8

379.262

346.666

23.907

12.247

6.733

5.04

9

32.409

55.335

37.6197

20.721

14.078

5.945

Table A.2 Percentage deviation of different parameters of GEN Bus 1 outgoing currents for LL fault at Bus 5

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

100

15.211

13.993

19.774

5.2

15.726

2

100

66.766

13.993

76.494

5.2

109.051

3

100

92.979

13.993

81.534

5.2

2323.788

4

100

119.936

13.993

379.765

5.2

1021.738

5

100

2429.487

13.993

933.977

5.2

115.739

6

100

2640.625

13.866

170.576

5.198

9.653

7

970

828.333

14.241

32.614

5.24

4.663

8

1035.023

346.666

23.907

12.247

6.733

5.04

9

32.124

55.335

37.619

20.721

14.078

5.945

Table A.3 Percentage deviation of different parameters of GEN Bus 1 outgoing currents for LG fault at Bus 6

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

99.999

6.485

6.1

8.5

5.2

15.726

2

99.999

46.783

6.1

56.007

5.2

109.051

3

99.999

98.876

6.1

69.347

5.2

323.788

4

99.999

96.056

6.1

655.622

5.209

1021.738

5

99.999

155.128

6.093

1822.703

5.2

1115.739

6

99.999

946.875

5.990

137.063

5.198

2323.788

7

1023.333

670

6.277

21.134

5.24

499.663

8

159.447

333.333

13.9

5.392

6.733

56.04

9

22.005

41.006

25.187

11.78

14.07

5.945

Table A.4 Percentage deviation of different parameters of GEN Bus 1 outgoing currents for LL fault at Bus 6

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

126.422

6.616

2.693

8.592

3.239

74.211

2

126.434

47.653

2.693

56.963

3.239

381.496

3

126.295

100.057

2.693

73.117

3.239

1408.286

4

126.116

582.984

2.693

788.769

3.240

2191.527

5

122.777

1029.487

2.693

956.976

3.241

539.941

6

33.676

2657.812

2.598

157.387

3.243

322.737

7

656.666

3427.5

1.988

1.738

3.125

5.418

8

696.774

1230.476

17.667

0.546

8.089

4.581

9

35.707

93.048

52.672

5.445

130.512

6.911

Table A.5 Percentage deviation of different parameters of GEN Bus 1 outgoing currents for LG fault at Bus 8

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

100

73.891

28.326

82.418

0.834

8.696

2

100

97.458

28.326

96.078

0.834

72.833

3

100

97.45

28.326

82.215

0.834

1849.149

4

100

2.02

28.32

666.465

0.834

1258.423

5

100

1211.538

28.32

4183.274

0.834

55.165

6

100

3746.875

28.153

279.911

0.835

0.265

7

1653.333

426.666

27.557

30.129

0.815

1.211

8

897.695

397.142

47.998

23.852

0.497

0.851

9

70.233

141.92

59.5433

46.231

3.758

0.789

Table A.6 Percentage deviation of different parameters of GEN Bus 1 outgoing currents for LL fault at Bus 8

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

100.001

63.067

15.64

72.928

6.908

70.302

2

100.001

96.476

15.64

96.027

6.908

368.089

3

100.001

97.781

15.64

81.741

6.908

6007.505

4

100.001

36.246

15.633

362.521

6.909

4125.426

5

100.001

6867.094

15.626

3910.138

6.909

123.891

6

100.001

3581.25

15.5194

229.469

6.91

6.233

7

3373.333

459.166

12.548

2.144

6.873

7.818

8

2081.566

190.476

52.742

0.078

3.065

7.331

9

49.998

23.475

76.8148

3.3026

63.272

9.51

Table A.7 Percentage deviation of different parameters of GEN Bus 2 outgoing currents for LG fault at Bus 5

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

100

15.693

7.92

20.23

0.834

8.696

2

99.999

72.465

7.92

80.349

0.834

72.833

3

99.999

99.852

7.92

71.922

0.834

1849.149

4

99.999

343.809

7.92

880.028

0.834

1258.423

5

99.999

327.444

7.92

2787.337

0.834

55.165

6

99.999

6348.437

7.756

293.552

0.835

0.265

7

1012.903

764.406

8.118

26.072

0.815

1.211

8

255.825

333.018

16.302

6.932

0.497

0.851

9

24.009

46.165

28.486

14.008

3.758

0.789

Table A.8 Percentage deviation of different parameters of GEN Bus 2 outgoing currents for LL fault at Bus 5

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

176.14

16.054

3.646

20.501

6.908

70.301

2

23.843

73.674

3.646

81.75

6.908

368.089

3

24.191

99.969

3.646

79.684

6.908

6247.505

4

23.548

469.85

3.646

838.199

6.909

4125.426

5

17.236

3584.858

3.646

3973.585

6.909

123.891

6

99.999

4396.875

3.511

277.772

6.91

6.233

7

570.967

433.898

2.098

1.541

6.873

7.818

8

810.194

229.245

23.07

0.346

3.065

7.331

9

41.975

4.294

56.409

5.066

63.272

9.51

Table A.9 Percentage deviation of different parameters of GEN Bus 2 outgoing currents for LG fault at Bus 6

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

100

13.691

16.14

17.893

5.2

15.726

2

99.998

62.987

16.14

73.073

5.2

109.051

3

99.999

100.156

16.14

75.927

5.2

2323.788

4

99.999

297.571

16.14

789.527

5.2

1021.738

5

99.999

3963.722

16.133

4319.746

5.2

115.739

6

99.999

2007.812

14.833

177.63

5.198

9.653

7

1158.064

851.694

15.156

34.101

5.24

4.663

8

343.689

356.603

25.814

13.13

6.733

5.04

9

34.934

57.3619

38.959

22.188

14.07

5.945

Table A.10 Percentage deviation of different parameters of GEN Bus 2 outgoing currents for LL fault at Bus 6

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

99.997

13.71

3.886

17.945

3.239

74.211

2

100

63.02

3.886

72.967

3.239

381.496

3

100

100.252

3.886

82.423

3.239

640.286

4

100

347.534

3.886

618.437

3.24

3191.527

5

100

4356.782

3.886

3879.476

3.241

4191.527

6

100

3170.312

3.778

179.494

3.243

5608.286

7

970.967

454.237

2.748

1.162

3.125

1595.418

8

1038.834

223.584

27.812

0.53

8.089

4.5817

9

28.497

9.815

53.081

4.055

130.512

96.911

Table A.11 Percentage deviation of different parameters of GEN Bus 2 outgoing currents for LG fault at Bus 8

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

99.999

40.078

24.780

49.328

5.2

15.726

2

100

89.154

24.78

92.201

5.2

109.051

3

100

98.293

24.78

71.016

5.2

2323.788

4

100

124.488

24.78

4514.134

5.2

1021.738

5

100

3890.536

24.746

3989.139

5.2

115.739

6

100

4165.625

24.601

288.689

5.1981

9.653

7

100

422.033

24.059

26.505

5.24

4.663

8

924.757

388.679

44.081

20.735

6.733

5.04

9

68.129

134.049

58.732

42.242

14.07

5.945

Table A.12 Percentage deviation of different parameters of GEN Bus 2 outgoing currents for LL fault at Bus 8

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

99.999

35.081

14.6

43.699

3.239

74.211

2

100

87.018

14.6

90.932

3.239

381.496

3

100

100.185

14.6

71.781

3.239

3408.286

4

100

253.926

14.6

1335.055

3.24

1391.527

5

100

4980.126

14.586

4084.586

3.241

939.941

6

1980.001

3089.0625

14.479

252.857

3.243

0.737

7

6583.87

457.627

11.621

1.749

3.125

5.418

8

2050.485

195.283

50

0.357

8.089

4.581

9

50.942

18.404

77.441

3.0815

130.512

6.911

Table A.13 Percentage deviation of different parameters of GEN Bus 3 outgoing currents for LG fault at Bus 5

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

100

15.693

23.04

20.2305

5.2

15.726

2

100

72.464

23.04

80.349

5.2

109.051

3

100

99.852

23.04

71.922

5.2

2323.788

4

100

343.809

23.04

880.028

5.2

1021.738

5

100

327.444

23.04

2787.337

5.2

115.739

6

100

3548.437

22.975

293.552

5.198

9.653

7

1558.62

764.406

23.346

26.072

5.24

4.663

8

657.758

333.018

33.932

6.932

6.733

5.04

9

47.09

46.165

54.88

14.008

14.07

5.945

Table A.14 Percentage deviation of different parameters of GEN Bus 3 outgoing currents for LL fault at Bus 5

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

100

16.054

12.053

20.501

3.239

74.211

2

100

73.6748

12.053

81.75

3.239

381.496

3

100

99.969

12.053

79.684

3.239

6408.286

4

100

469.85

12.053

838.199

3.24

4191.527

5

100

3584.858

12.046

3973.585

3.241

139.941

6

100

4396.875

11.941

277.772

3.243

0.737

7

2396.551

433.898

9.418

1.541

3.125

5.418

8

1694.827

229.245

49.472

0.346

8.089

4.581

9

45.573

4.294

72.48

5.066

130.512

6.911

Table A.15 Percentage deviation of different parameters of GEN Bus 3 outgoing currents for LG fault at Bus 6

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

99.999

13.691

19.173

17.893

0.834

8.696

2

99.999

62.987

19.173

73.073

0.834

72.833

3

99.999

100.156

19.173

75.927

0.834

1849.149

4

99.999

297.571

19.173

789.527

0.834

1258.423

5

99.999

3963.722

19.180

4319.746

0.834

55.165

6

99.999

2007.812

29.772

177.63

0.835

0.265

7

1217.241

851.694

9.651

34.101

0.815

1.211

8

412.5

356.603

29.803

13.13

0.497

0.851

9

42

57.361

46.982

22.332

3.758

0.789

Table A.16 Percentage deviation of different parameters of GEN Bus 3 outgoing currents for LL fault at Bus 6

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

100

13.710

7.2

17.945

6.908

70.301

2

100

63.020

7.2

72.967

6.908

368.089

3

100

100.252

7.2

82.423

6.908

6247.505

4

100

347.534

7.2

618.437

6.909

4125.426

5

100

7356.782

7.193

3879.476

6.909

123.891

6

100

1170.312

7.11

179.494

6.9103

6.233

7

1755.172

454.237

5.313

1.162

6.873

7.818

8

1338.793

223.584

40.259

0.53

3.065

7.331

9

34.241

9.815

60.588

4.055

63.272

9.51

Table A.17 Percentage deviation of different parameters of GEN Bus 3 outgoing currents for LG fault at Bus 8

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

99.999

40.0781

6.18

49.328

5.2

15.726

2

99.9999

89.154

6.18

92.201

5.2

109.051

3

99.999

98.293

6.18

71.016

5.2

2323.788

4

99.999

307.103

6.18

4342.718

5.2

1021.738

5

99.999

1890.536

6.18

3989.139

5.2

115.739

6

99.999

3165.625

6.037

288.689

5.198

9.653

7

958.62

422.033

5.73

26.505

5.24

4.663

8

209.051

388.679

17.883

20.735

6.733

5.04

9

99.018

134.049

41.227

42.242

14.07

5.945

Table A.18 Percentage deviation of different parameters of GEN Bus 3 outgoing currents for LL fault at Bus 8

DWT level

Sa

Sd

Ka

Kd

RMSa

RMSd

1

99.999

35.081

3.126

43.699

3.239

74.211

2

99.999

87.018

3.126

90.932

3.239

381.496

3

811.416

100.185

3.126

71.787

3.239

2408.286

4

1549.476

253.926

3.126

1335.055

3.240

2191.527

5

3155.999

3980.126

3.126

2984.586

3.241

139.941

6

3199.999

3089.062

3.058

252.8574

3.243

0.737

7

4568.965

457.627

1.822

1.749

3.125

5.418

8

633.189

195.283

19.281

0.357

8.089

4.581

9

46.31

18.404

56.94

3.081

130.512

6.911

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