Potentials - January/February 2016 - 39

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.

Doubly fed transmission lines

the algorithm was implemented in
the same and has been used for the
fault analysis and fault classification. The transmission line faults in
a power system are classified as the
line to line (L-L), three-phase symmetrical (L-L-L), three-phase symmetrical ground (L-L-L-G), single
line to ground (L-G), and double line

from the signal x (t) by use of the
mother wavelet } (t).
The DWT of a signal x (t) is given
by
+3

c jk =

#
-3

x (t)

1
t - k2 j
}a
dt,
j
2j k
2

(1)

where j is the scale parameter and k
Doubly fed transmission lines are
is the shift parameter, both of which
widely used in modern power systems because of their many advantages, such as system stability
improvement, an increase in transmitted power, a reduction in transmission losses, an enhancement in
voltage control, and increased loading capacity of the line. Such lines
are usually injected with power from
either end of a transmission line.
are integers. c jk is defined as the
During the occurrence of a fault on
ground (L-L-G) faults. We present a
wavelet coefficient of the transient
the transmission line, the fault curnew fault classification technique
time-domain signal x (t), which can
rents from both ends flow in the line
for a transmission line with sources
be seen as the convolution of the sigto the point of fault occurrence. Figon both sides and also prove the efnal x (t) with a dilated, reflected, and
ure 1 shows a doubly fed transmisficacy of the Db4 wavelet for accurate
normalized version of the mother
sion line with buses on both ends
fault classification.
wavelet. The scale and time shift of
and a load connected to one end.
Wavelet transform and MRa
the mother wavelet are determined
With the addition of a second voltWavelet transform is a potential tool
by the parameters j and k. We can
age bus at the other end of the line,
for the application to a power sysadjust the resolution of the signal in
the process of fault classification betem. A concise introduction to the
both time and frequency domains to
comes more complex. A fault classifidiscrete wavelet transform (DWT)
effectively study/extract signal
cation algorithm is proposed in this
and MRA is given here. c is defined
parameters-a useful analysis techarticle, using the currents from both
as the wavelet coefficient, obtained
nique that the Fourier transform
ends of the transmission line. The
could not provide.
current signals are then
The application of DWT
passed through wavelet
is coupled with MRA.
MRA, which decomposes
Bus 1
Transmission Line
Bus 2
Through MRA, a signal can
the signal into fixed-frebe decomposed and studied
quency bands by passing it
in various frequency bands
through successive stages
Fault
Load
with sufficient resolution.
of lowpass filters and highThe source signal is decompass filters. As shown by
posed into an approximaChanda et al., in the event fig1 A doubly fed transmission line.
tion component (obtained
of fault occurrence, the
by passing through the lowsecond and third harmonpass filter) and a detail comics in the transient signal
Signal
ponent (obtained by passare dominant. For a saming through the highpass
pling frequency of 3 kHz,
filter). The approximation
these harmonics are locatd1 (750-1,500 Hz) HP
LP a1 (0-750 Hz)
and detail components are
ed in the fourth level detail
further individually decomcoefficients of the wavelet
d2 (375-750 Hz) HP
LP a2 (0-375 Hz)
posed into another approxiMRA filter bank (Fig. 2).
mation and detail compoThe fourth-level detailed
nent each, and the process
coefficients of the curd3 (187.5-375 Hz) HP
LP a3 (0-187.5 Hz)
is repeated until the secrent signals are extracted
ond and third harmonic
in this process, and they
components are extracted.
are used for fault classid4 (93.75-187.5 Hz) HP
LP a4 (0-93.75 Hz)
The subsequent stages of
fication in our algorithm.
decomposition are called
The line was modeled in
levels.
MATLAB software, and fig2 The stages of MRA on a signal.

The choice of the mother wavelet plays an
important role for fault detection and
classification in the transmission line.

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