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RBF AND SVM NEURAL NETWORKS
FOR POWER QUALITY
DISTURBANCES ANALYSIS
Przemysław Janik, Tadeusz Łobos
Wroclaw University of Technology
Peter Schegner
Dresden University of Technology
Contents

Increased Interest in Power Quality

RBF and SVM Neural Networks

Space Phasor

Basic Disturbances


Simulation of Voltage Sags
Conclusion
2
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
3
Interconnections
internal
disturbances
in power grid
electrical
power grid
disturbance
source
disturbance
sink
4
Space division by classical BP
algorithm and RBF network
Back Propagation Algorithm
RBF Neural Network
5
Radial Basis Function
rbf
 xx
cnt
 x  xcnt
  exp   2c2

2




x   xi , x j 
rbf
xj
xi
6
Radial Basis Function RBF
Neural Network

Formulation of the Classification Problem
W r  x   0 dla x  X

W r  x   0 dla x  X

T
T
X+, X- classes
x
input vector

radial function
7
SVM Neural Networks
Support Vector Machines

Formulation of the Classification Problem
 xi , di 
w xi  b0  1  di  1
T
0
w xi  b0  1  di  1
T
0
8
Learning of SVM networks

Hyperplane Equation
g  x  w x  b  0
T

Finding the Minimum
1 T 
min  w w 
w 2



d i w xi  b  1
T
9
Dividing hyperplane and
separation margin
g  x   wT x  b  0
Support Vectors
Separation Margin
10
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)
11
Space Phasor (SP)
 f1 
f 
 2
2
3
1


0


f 
1

2
3
1
2

2
 f

a



f
 b
3 
fc 


2 
f1  jf 2
2
12
Basic Disturbances








Outages (Duration and
Frequency)
Sags
Swells
Harmonics
Flicker (Voltage
Fluctuation)
Oscillatory transients
Frequency variation
Symmetry
13
Parametric equations of
basic disturbances
Event
Pure
Sinusoid
Sudden
Sag
Sudden
Swell
Equation
v  t   sin(t )


v  t   A 1    u  t1   u  t2   sin t 


v  t   A 1    u  t1   u  t2   sin t 
Harmonics
v  t   A 1 sin t    3 sin  3t    5 sin  5t    7 sin  7t  
Flicker
v  t   A 1   sin  t   sin t 
Oscillatory
Transient

v t   A sin t    expt t1  / sin n t  t1  

14
Parameters variation
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
Signals number
In each class:
50
Totally:
300
15
Voltage sags
1.5
1
1
imaginary part
U [p.u.]
0.5
0
0.5
0
-0.5
-0.5
-1
-1
0
0.02
0.04
0.06
time [s]
Sags deepness
Sags duration
0.08
0.4
0.032 s
0.1
-1.5
-1.5
-1
-0.5
0
real part
0.5
1
1.5
16
Oscillations
2
1.5
1.5
1
imaginary part
1
U [p.u.]
0.5
0
0.5
0
-0.5
-0.5
-1
-1
-1.5
0.02
0.04
0.06
time [s]
Time constant
Oscillations period
0.08
0.1
0.0176 s
0.0053 s
-1.5
-2
-1
0
real part
1
2
17
Flicker
1.5
1
1
Imaginary part
1.5
U [p.u]
0.5
0
0.5
0
-0.5
-0.5
-1
-1
-1.5
0
0.05
0.1
time [s]
0.15
-1.5
-1.5
-1
-0.5
0
real part
0.5
1
1.5
Flicker amplitude 0.12
Frequency
8 Hz
18
TEST
SIGNALS (40)
Classification results of SVM
CLASSES
FLICK
HAR
SIN
SWELL
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
SAG
0.025
0.0
0.0
0.0
0.0
0.975
19
Classification results of RBF
TEST
SIGNALS (40)
SIN
SWELL
CLASSES
FLICK
HAR
0.0 0.975 0.0
0.0
0.725
OSCILL
SAG
0.0
0.0
0.0
0.0
0.0
0.0
0.0
SIN
1.0
SWELL
0.275
FLICK
0.0
0.0
1.0
0.0
0.0
HAR
0.025
0.0
0.0
0.975
0.0
OSCILL
0.350
0.0
0.0
0.0
0.650
SAG
0.275
0.0
0.0
0.0
0.0
1.0
0.0
0.0
0.975
0.725
Classification results of SVM
20
Sags originating in faults
SYS: Sk''  3 GVA, U N  110 kV
2800 different signals
faults ABC AB BC CA
T1: n  110/16,5 d/y
L1: l  0,5...2,5 km, l  0,5 km
ts: t z  0,051...0,61 s, ts  0,04 s
L1
Short circuit
ODB 1
S3
SYS
S1
T1 S2
L2
ODB 2
S4
21
Voltage sags
4
4
1.5
x 10
1.5
1
imaginary part
1
0.5
U [V]
0
0.5
0
-0.5
-0.5
-1
-1
-1.5
0
x 10
0.02
0.04 0.06
time [s]
0.08
0.1
-1.5
-1.5
-1
-0.5
0
real part
0.5
1
1.5
4
x 10
22
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
23