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RBF AND SVM NEURAL NETWORKS FOR POWER QUALITY
DISTURBANCES ANALYSIS
Przemysław Janik, Tadeusz ŁobosWroclaw University of Technology
Peter Schegner Dresden University of Technology
2
Contents Increased Interest in Power
Quality RBF and SVM Neural Networks Space Phasor Basic Disturbances Simulation of Voltage Sags Conclusion
3
Interest in Power Quality Deregulation of the electric
energy market Growing need for
standardization Equipment has become more
sensitive Equipment causes voltage
disturbances Power quality can be measured
4
Interconnections
internaldisturbances in power grid
electricalpower grid
disturbancesink
disturbancesource
5
Space division by classical BP algorithm and RBF network
Back Propagation Algorithm
RBF Neural Network
6
Radial Basis Function
2
2exp
2cnt
rbf cnt
x xx x
c
,i jx x x
ixjx
rbf
7
Radial Basis Function RBF Neural Network
Formulation of the Classification Problem
0 dla
0 dla
Tr
Tr
X
X
W x x
W x x
X+, X- classesx input vector radial function
8
SVM Neural NetworksSupport Vector Machines
Formulation of the Classification Problem
0 0
0 0
1 1
1 1
Ti i
Ti i
b d
b d
w x
w x
,i idx
9
Learning of SVM networks
Hyperplane Equation
0Tg b x w x
Finding the Minimum
1min
2T
w
w w 1Ti id b w x
10
Dividing hyperplane and separation margin
0Tg b x w x
Separation Margin
Support Vectors
11
SVM characteristics linearly not separable data sets can be
transformed into high dimensional space to be separable (Cover’s Theorem)
Avoiding of local minima (quadratic programming)
Learning complexity doesn't depend on data set dimension (support vectors)
SVM network structure complexity depends on separation margin (to be chosen)
12
Space Phasor (SP)
a1
b2
c
1 1f1
2 2 2f
3 3 3f0
2 2
f
f
1 2
2
f jff
13
Basic Disturbances Outages (Duration and
Frequency) Sags Swells Harmonics Flicker (Voltage
Fluctuation) Oscillatory transients Frequency variation Symmetry
14
Parametric equations of basic disturbances
sin( )v t t
1 21 sinv t A u t u t t
1 21 sinv t A u t u t t
1 3 5 7sin sin 3 sin 5 sin 7v t A t t t t
1 sin sinv t A t t
1 /1sin exp sint t
nv t A t t t Oscillatory Transient
Flicker
Harmonics
Sudden Swell
Sudden Sag
Pure Sinusoid
EquationEvent
15
Parameters variation
Signals numberIn each class: 50Totally: 300
Event Parameters variation
Pure Sinusoid All parameters constant
Sudden Sag duration 0-9 T, amplitude 0.3-0.8 pu
Sudden Swell duration 0-8 T, amplitude 0.3-0.7 pu
Harmonics order 3,5,7, amplitude 0-0.9 pu
Flicker frequency 0.1-0.2 pu, amplitude 0.1-0.2 pu
Oscillatory Transient
time const. 0.008-0.04 s, period 0.5-0.125 pu
16
Voltage sags
Sags deepness 0.4 Sags duration 0.032 s
0 0.02 0.04 0.06 0.08 0.1-1
-0.5
0
0.5
1
time [s]
U [p
.u.]
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
real part
imag
inar
y pa
rt
17
Oscillations
Time constant 0.0176 s Oscillations period 0.0053 s
0.02 0.04 0.06 0.08 0.1-1.5
-1
-0.5
0
0.5
1
1.5
2
time [s]
U [p
.u.]
-2 -1 0 1 2-1.5
-1
-0.5
0
0.5
1
1.5
real part
imag
inar
y pa
rt
18
Flicker
Flicker amplitude 0.12 Frequency 8 Hz
0 0.05 0.1 0.15-1.5
-1
-0.5
0
0.5
1
1.5
time [s]
U [p
.u]
-1.5 -1 -0.5 0 0.5 1 1.5-1.5
-1
-0.5
0
0.5
1
1.5
real part
Imag
inar
y pa
rt
19
Classification results of SVM
CLASSES
SIN SWELL FLICK HAR OSCILL SAG
SIN 1.0 0.0 0.0 0.0 0.0 0.0
SWELL 0.025 0.975 0.0 0.0 0.0 0.0
FLICK 0.0 0.0 1.0 0.0 0.0 0.0
HAR 0.025 0.0 0.0 0.975 0.0 0.0
OSCILL 0.0 0.0 0.0 0.0 1.0 0.0
TE
ST
SIG
NA
LS
(40
)
SAG 0.025 0.0 0.0 0.0 0.0 0.975
20
Classification results of RBF
CLASSES
SIN SWELL FLICK HAR OSCILL SAG
SIN 1.0 0.0 0.0 0.0 0.0 0.0
SWELL 0.275 0.725 0.0 0.0 0.0 0.0
FLICK 0.0 0.0 1.0 0.0 0.0 0.0
HAR 0.025 0.0 0.0 0.975 0.0 0.0
OSCILL 0.350 0.0 0.0 0.0 0.650 0.0
TE
ST
S
IGN
AL
S (
40)
SAG 0.275 0.0 0.0 0.0 0.0 0.725
0.975
1.00.975
Classification results of SVM
21
Sags originating in faults
SYS S1 S2
S3
S4
L1
L2
Short circuit
T1
ODB 1
ODB 2
''SYS: 3 , 110
T1: 110/16,5 d/y
L1: 0,5...2,5 , 0,5
ts: 0,051...0,61 , 0,04
k N
z s
S GVA U kV
n
l km l km
t s t s
2800 different signals
faults ABC AB BC CA
22
Voltage sags
0 0.02 0.04 0.06 0.08 0.1-1.5
-1
-0.5
0
0.5
1
1.5x 10
4
time [s]
U [
V]
-1.5 -1 -0.5 0 0.5 1 1.5
x 104
-1.5
-1
-0.5
0
0.5
1
1.5x 10
4
real part
imag
inar
y pa
rt
23
Conclusion and future prospects Automated PQ assessment
needed SVM based classifier appropriate
for automated PQ disturbances recognition
Network models for wide parameter changes
Research work do be done with real signal