1
Fault-Induced Transient Detection
Based on Real-Time Analysis of the
Wavelet Coefficient Energy
Prof. Flavio B. Costa (UFRN - Brazil)
Goal
• Wavelet-Based Method for Real-Time Detection of
Fault-Induced Transients
– Energy of the wavelet coefficients with Border
Distortions
• Contributions over other Wavelet-Based Methods
– Presents no time delay in real-time analysis
– Is not affected by the choice of the mother wavelet
– Presents a reliable performance even in critical
cases
1.3
1.0
Signal sliding
window
0.5
Circular signal sliding
window
Sample that does
not exist at the
current sampling
Sample
0
1.3
-1.0
-1.3
Wavelet sliding
window
Sample
Current
sampling
0
x( k)
-1.3
The first L-1
coefficients are not
computed in real-time
Coefficients with border
distortions of the signal
sliding window
Real-time wavelet
coefficient energy
Wavelet sliding
window
Current (pu)
-0.5
Real-time
wavelet coefficients
Original signal (pu)
Boundary Wavelet Coefficient Energy
Wavelet coeff.
of the MODWT
pyramid
algorithm
Coefficient to be
computed in the
next sampling
k-3
db(4)
~
h(0) = -0.0915
~
h(1) = -0.1585
~
h(2) = 0.5915
~
h(3) = -0.3415
k-2
k-1
k
k-∆k+1
k-∆k+3
k-∆k+2
Sample
~
h(2)
~
h(2)
~
h(2) ~
~ ~
h(2)
0 h(0)0 h(0) ~
~
h(0)
~ h(1)
~~h(3)
~0 ~ x(k) h(0)
~
h(1) h(1) h(3)0 h(1)
~ ~
h(3) h(3)
(kx)( k)
x
x(k)
k-3
k-∆k+3
k-2 k-1
k
kk
Real-Time Fault-Induced Transient Detection
0
-3
10 6
10 5
10 4
10 3
10
kF
Fault
inception
time
detection
Energy due to
border effects
Sample
Energy due to
noises and
transients
2
1
10
10 0
10 5
Fault inception time
followed by transients
5
3
kF
Normalized wavelet coefficient energy
Normalized wavelet
coefficient energy
Current (kA)
db(4)
db(6)
db(90)
db(6) - db(90)
10 4
10
10
10
Sample
10
No time delay in
fault detection for
compact wavelets
3
2
1
Time delay in
fault detection
for long wavelets
0
kF -7 kF
Sample
kF +37 kF -7 kF
No time delay in
fault detection for
compact and long
wavelets
Sample
kF +37
Wavelet coefficient energy
Wavelet coefficients
Current (pu)
Real-Time Fault-Induced Transient Detection
7
5
Fault inception time
followed by transients
Fault clearance time
0
-5
-7
kF
Sample
kF
Sample
25
0
-25
107
Fault inception
time detection
106
Energy due to
border effects
Energy due to
noises and transients
105
104
3
10
2
10
kF
Sample
Real-Time Fault-Induced Transient Detection
Bus 1
CB3
line 2
CB4 Bus 2
S1 Z
1
CB5
CB1
CCVT
CT
line 1
CB2
Bus 3
line 3
Fault
•
Evaluated parameters:
• fault type
• fault resistance
• fault distance
• fault inception angle
• sampling rate
• effect of the mother
wavelet
• etc.
2698 faults were simulated
CB7
S2
CT
CCVT
Fault
Fault-induced
transient detection
•
CB6
T1
Fault-induced
transient detection
Time delay (samples)
Success rate (%)
Mother
wavelet
w
Ewb
Ew
w
Ew
Haar
0.5
0.4
0.2
96.9
100
db(4)
0.2
0.8
0.2
99.0
100
db(6)
0.3
1.0
0.2
98.9
100
db(12)
0.7
1.8
0.2
98.2
100
db(24)
2.0
3.0
0.2
97.9
100
db(48)
5.0
5.6
0.2
93.9
100
coif(6)
0.7
1.6
0.2
97.5
100
coif(12)
2.0
3.3
0.2
96.7
100
coif(18)
3.9
4.8
0.2
96.4
100
coif(24)
5.8
6.6
0.2
96.1
100
coif(30)
8.0
8.3
0.2
95.6
100
Real-Time Fault-Induced Transient Detection
Features
w
Ewb
The most sensible to fault-induced transients
Affected by low-frequency oscillations
Ew
√
√
√
√
The most reliable fault detection with the choice of the mother wavelet
√
No time delay with the choice the mother wavelet
√
No time delay with the decomposition level
√
The most reliable detection overdamped fault-induced transients
√
Fault-induced transient detection not affected by current transformer saturation
√
√
√
FLOPs per sampling
2L-1
2L+2
2L2+2
Not affected by fault inception angle
√
Not affected by fault resistance
√
√
√
Not affected by fault distance
√
√
√
Not affected by the fault type
√
√
√
Not affected by mutually coupled line
√
√
√
The least affected by the sampling rate
√
Fault-Induced Transient Detection Based on
Real-Time Analysis of the Wavelet
Coefficient Energy
Flavio Bezerra Costa
flaviocosta@ect.ufcg.br
Federal University of Rio Grande do Norte
School of Science and Technology
Campus Universitário Lagoa Nova - Natal - RN
59078-970, Natal - RN - Brazil
Phone: +55 (84) 3342-2362
http://www.ect.ufrn.br