Potentials - January/February 2016 - 42
Table 2. The tabulation of a fault classification algorithm using
different wavelet fault types: L-L fault (RY fault).
M r12 + M y12 + (M r1 - M r2)
M b12 . 0
.0
(yes/no)
(yes/no)
(M y1 - M y2) (M b1 - M b2)
Fault
.0
.0
(yes/no)
(yes/no) identiFied
Wavelet
used
M r1
M y1
M b1
M r2
M y2
M b2
Db2
2.078
-1.811
-0.266
0.334
0.320
0.012
No
No
No
No
-
Db4
1.7212
-1.413
-0.307
-0.170
0.3208
-0.150
Yes
No
No
Yes
RY
Db6
-0.518
0.596
-0.078
-0.174
0.346
-0.172
Yes
No
No
Yes
RY
Db8
-0.621
0.403
0.218
-0.023
-0.141
0.165
Bior 1.3
7.413
-7.371
-0.041
-5.028
4.762
0.267
Yes
Yes
No
No
No
No
Yes
No
RY
RYB
Bior 2.2
-0.051
0.477
-0.426
-0.872
1.466
-0.593
Yes
No
No
Yes
RY
Bior 3.1
2.379
-1.721
-0.658
-2.174
2.809
-0.634
Yes
No
No
Yes
RY
Bior 4.4
-0.792
0.704
0.088
-0.528
0.593
-0.064
Yes
Coif 2
-0.538
0.514
0.023
0.727
-0.784
0.056
Yes
No
No
Yes
No
No
Yes
RB
RY
Coif 3
2.007
1.558
0.448
1.169
-1.566
0.397
No
No
No
Yes
-
RY
Coif 4
-1.181
0.883
0.298
0.253
-0.473
0.219
Yes
No
No
Yes
Coif 5
-0.388
0.166
0.221
-0.270
0.103
0.166
Yes
Yes
Yes
Yes
-
sym 2
2.0780
-1.811
-0.266
0.334
-0.346
0.012
Yes
No
No
No
RYB
sym 3
2.743
-2.090
-0.652
-2.437
3.127
-0.690
Yes
No
No
Yes
RY
sym 4
-2.231
2.218
0.012
2.451
-2.499
0.048
Yes
No
No
Yes
RY
sym 5
1.358
-1.518
0.160
-2.022
1.928
0.093
Yes
No
No
Yes
RY
doubly fed transmission line model
was designed using MATLAB SIMULINK, and wavelet MRA was implemented using the wavelet toolbox.
Simulations were performed for different types of faults, fault distances,
and fault inception angles.
Table 1 illustrates the fault classification algorithm used for our analysis.
For the results tabulated in Table 1, we
have used Db4 as the mother wavelet.
For example, when an RY fault occurs, the values of M r1, M y1 , and M b1
(at bus 1) are 1.7212, -1.413, and
Therefore, it is an L-L fault according to
our algorithm. We then check whether
eM r1 - M r2 e . 0. If it does not, we check
whether eM y1 - M y2 e . 0. If the answer
is "no," we check if eM b1 - M b2 e . 0.
Here, eM b1 - M b2 e . 0, so it is an RY
fault. For different types of faults, various cases have been extensively investigated with different fault distances
and fault inception angles.
Tables 2-4 show the results
of comparisons between different standard wavelets, namely,
Daubechies (Db2, Db6, and Db8),
We have investigated the results obtained from
the wavelet MRa of the fault current signal using
16 wavelets, and we have arrived at the one that
is most suitable, which is the db4 wavelet.
-0.307. Similarly, the values of M r2,
M y2 , and M b2 (at bus 2) are -0.170,
0.3208, and -0.150. The values of
M r12, M y12, and M b12 are calculated as
1.5512, -1.0922, and -0.457. We then
check whether or not the summation
of M r12, M y12 , and M b12 is 0. For this
case, the sum of these values is 0.002.
42
n
J a n u a r y/Febr uar y 2016
Biorthogonal (Bior 1.3, Bior 2.2,
Bior 3.1, and Bior 4.4), Coiflets (Coif
2, Coif 3, Coif 4, and Coif 5), and
Symlets (Sym 2, Sym 3, Sym 4, and
Sym 5) for a particular type of fault.
We have illustrated results regarding the performance of the different wavelets for fault classification.
IEEE PotEntIals
A total of four tables representing
each type of fault, namely the L-G,
L-L, L-L-G, and L-L-L faults, have
been presented.
For instance, when Db4 is used
as the mother wavelet and a YBG
fault occurs, the values of M r1, M y1,
and M b1 (at bus 1) are 0.725, -1.753,
and 0.561. Similarly, the values
of M r2, M y2, and M b2 (at bus 2) are
0.796, 0.728, and -1.029. The values
of M r12, M y12, and M b12 are calculated
as 1.521, -1.025, and -0.468. We
then see whether or not the summation of M r12, M y12 , and M b12 is 0.
For this case, the sum of these values is 0.028 (not 0). Therfore, it is
an L-G or an L-L-G fault, according
to our algorithm. We calculate D r12,
D y12 , and D b12 as 0.071, 1.025, and
0.468, respectively. Now, we evaluate whether D r12 . D y12, and if not,
we check if D y12 . D b12 . If it does not,
we see whether D b12 . D r12, and if the
answer is "no," we proceed to check
which of the three values (D r12, D y12,
and D b12) is the least. Here, D r12 is
the least value, so it is a YBG fault.
Similarly, for all other types of faults,
different cases have been extensively
investigated, and our results were
found to confirm that for the Db4
Table of Contents for the Digital Edition of Potentials - January/February 2016
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