# 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

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

Electrical Engineering Department, GKCIET, Malda, India

Page:
10-18
|
DOI:
https://doi.org/10.18280/mmc_a.931-402
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

## 3.1.png

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.

## 2.png

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

## 3.png

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.

## 4.png

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.

## 5.png

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

## 6.png

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.

## 7.png

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.

## 8.png

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

## 9.png

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).

## 10.png

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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