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

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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

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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