189 - Wavelet, Kalman Filter and Fuzzy-Expert Combined System for Classifying Power System Disturbances

7/28/2019 189 - Wavelet, Kalman Filter and Fuzzy-Expert Combined System for Classifying Power System Disturbances

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Proceedings of the 14th International Middle East Power Systems Conference (MEPCON10), Cairo University, Egypt, December 19-21, 2010, Paper ID 189.

398

Wavelet, Kalman Filter and Fuzzy-Expert Combined

System for Classifying Power System Disturbances

A. A. Abdelsalam1,*, A. A. Eldesouky2, A. A. Sallam, Member, IEEE2

[email protected], [email protected], [email protected]

Abstract: A new algorithm for power system disturbanceclassification is proposed in this paper. It is a two-stage system

that employs the great potentials of the discrete wavelet

transform (DWT), Kalman filter and a fuzzy-expert system. For

the first stage, the captured voltage waveform is passed through

the DWT to determine the noise inside it. The covariance of this

noise is then calculated and fed together with the captured

voltage waveform to the Kalman filter to provide the amplitude

and the slope of this waveform. These are considered as an input

to the fuzzy-expert system in the second stage to determine the

class to which the waveform belongs. Simulation and

experimental results confirm the aptness and the capability of the

proposed system in power system disturbance detection and

classification.

keywords: Power quality, DWT, Kalman filter, Fuzzy expertsystem, Power System Disturbance.

I. INTRODUCTIONAny variation in voltage, current or frequency which may lead

to an equipment failure or malfunction is potentially a powerquality problem. The widespread use of electronic equipment,

such as information technology equipment, power electronics

such as adjustable speed drives, programmable logiccontrollers, energy-efficient lighting, have led to a change in

the nature of electric loads. These loads are simultaneously the

major causes and the major victims of power quality

problems. Due to their non-linearity, all these loads cause

disturbances in the voltage waveform.One critical aspect of power quality (PQ) studies is the

ability to perform automatic power quality data analysis and

classification. An important step in understanding and henceimproving the quality of electric power is to extract sufficient

information about the events that cause the power quality

issues.A number of techniques have been investigated in literature

for automatic classification of different types of power quality

events. Such an automated PQ assessment requires a high

level of engineering expertise and powerful tools. A number

of papers based on different techniques for

________________________________________________* Corresponding author

detection and classification of power quality phenomena have

been published over the past years. Theoretical foundations of

voltage disturbances are for example described in [1-3].

Wavelet analysis has been used for identification of powersystem disturbances. The use of wavelets permits the study of

a signal with different time-frequency resolution. Use of the

coefficients of the high frequency decomposition of thediscrete wavelet transform (DWT) has been proposed in the

literature for identification and estimation of the related

parameters of a voltage event [4-6]. In [7] an algorithm based

on the energies of decomposed signals from wavelet multi

resolution analysis (MRA) was proposed to distinguishdifferent classes of power quality events. This algorithm had

drawback that the phase shifts of the signals studied were not

considered despite their impact on the results.

Using the change in magnitude of the fundamentalcomponent of supply voltage, Kalman filter can be employed

to detect and to analyse voltage event [8-9]. The results of

Kalman filter depend on the model of the system used and the

suitable selection of the filter parameters. If the selection ofthe Kalman filter parameters is not suitable, the rate of

convergence of the results will be slow or the results will

diverge.Expert systems have been proposed to identify, classify and

diagnose power system events successfully for a limited

number of events [9-11]. Rules based expert systems are

highly dependent on if ..then clauses. If many event types orfeatures are analyzed, the expert system would become more

complicated and risks of losing selectivity would increase.

Another drawback is that these systems are not alwaysportable due to the settings that depend mostly on the designer

or operator of the systems for a particular set of events.

A two stage system for classifying the power system

disturbances is proposed in this paper. In the first stage, the

captured voltage waveform is passed through DWT to identifyits noise. The covariance of this noise together with the

captured voltage waveform is fed to the Kalman filter to

enhance and speed up its rate of convergence. In the second

stage, the outputs of the Kalman filter; the amplitude of thecaptured voltage waveform and its rate of change with time

(slope), are passed through a fuzzy expert system that

identifies the class to which the disturbance waveform

2Dept of Electrical Engineering, Port-Said

University, Port-Said, 42523, Egypt

1Dept of Electrical Engineering, Suez Canal

University, Ismailia, 41522, Egypt


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belongs. Several digital simulation results using MATLAB

[12] and practical test waveform are presented to satisfy andensure the capability of the proposed system for classifying

the disturbances successfully.

II. THE PROPOSED SYSTEMThe proposed system which consists of two stages as

mentioned above is shown in Fig. 1. The two stages are

performed with each new voltage sample; (i) evaluating a newvalue of the amplitude and slope using Kalman filter with thehelp of DWT, (ii) classifying the disturbance using fuzzy-

expert system according to the evaluated values.

Fig. 1 Block diagram for the proposed technique

2.1 Wavelet Transform

Wavelet transform is a useful tool in signal analysis. The

continuous Wavelet Transform(WT) of a signalx(t) is defined

as [13].

= dt

a

bttx

aX

ba)()(

1,

(1)

)(1

)(,

a

bt

at

ba

= (2)

where ()is the mother wavelet, and other wavelets are itsdilated and translated versions, where a and b are the dilation

parameter and translation parameter respectively,The discrete WT (DWT) Calculations are made for

chosen subset of scales and positions. This scheme is

conducted by using filters and computing the so called

approximations and details. The approximations (A) are the

high-scale, low frequency components of the signal. The

details (D) are the low-scale, high-frequency components. The

DWT coefficients are computed using the equation:

==Zn

kjkjbangnxXX ][][

,,,(3)

where a=2j, b=k2j, jN, k

N. The wavelet filtergplays therole of.

The covariance of the details (D) is determined to be

considered as an initial input to the Kalman filter.

2.2 Kalman Filter

Kalman algorithm is applied in order to compute theamplitude of the waveform. The Kalman filtering performs the

following operations [14]..

First of all, it is necessary to have a mathematical

description both of the system and of the measurement. Theprocess will be estimated at time t+1 based on the knowledge

of the a-priori process at time tk.

kkKkwxx +=+ 1 (4)

Next, the state variables and the stochastic system model

will be defined. It is assumed that the signal system under

study (voltage signal) corresponds to a sinusoidal signal as is

expressed in the following equation:

)sin( += TkAsk

(5)

For the next time step k+1:

))1(sin(1

++=+ TkAsk (6)

Considering the state variables as the following:

)cos(,1

Axk=

)sin(,2

Axk= (7)

The following relationship can be obtained:

kk

k

x

x

x

xx

=

=

+

+

2

1

12

1

1

10

01(8)

where is the angular frequency =250 rad/s, and T is thesampling interval.

Consequently, the measurement at time k+1 may be

related with the state variables at time k+1, as:

+

+=+

2

1

1))1(cos(

))1(sin(

x

x

Tk

Tkz

T

k

11 ++= kk xH (9)

whereHis the Matrix giving the ideal connection between themeasurement and the state vector at time tk.

The measurement of the process is assumed to occur at

discrete points in time in accordance with the linear

relationship:kkkk

vxHz += (10)

where vk is the measurement error which is evaluated byDWT.

The random process can be modeled by:

kkkxx

1=

+ (11)

The estimation of the process covariance,P, in the next time

step k+1 can be obtained by the following equation:

k

T

kkkk QPP +=+ 1 (12)

kQ is the covariance matrix ofwk and is assumed to be equal

to the identity matrix in this model.

The Kalman gain,K, can be computed as:( ) 1 +=k

T

kkk

T

kkkRHPHHPK (13)

Rk is the covariance matrix of vk . the value ofRk is not

assumed but it is considered the covariance of the detailscoefficients of the first level of DWT of the measurement

signal.

With this information the state estimation can be updated

knowing the measured

( ) +=kkkkkk

xHzKxx (14)


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and the process covariance can be updated according to:

( ) =kkkk

PHKIP (15)

The waveform amplitude is directly computed at any time

instant kfrom the estimated state variables as follows:

kkxxA )( 2

2

2

1+= (16)

and the slope is obtained from the following relationship:

T

AA

Skk

k

=

)( 1(17)

where: Ak, Ak-1 are the waveform amplitudes at the time

instants kand k-1 respectively.

2.3 Fuzzy-Expert Systems

It is usually appropriate to use fuzzy logic when amathematical model of a process doesn't exist or does exist but

is too difficult to encode and too complex to be evaluated fast

enough for real time operation. The accuracy of the fuzzy

logic systems is based on the knowledge of human experts;

hence, it is only as good as the validity of the rules. As thepower system data is highly uncertain and the power

disturbance monitoring is a pattern classification problem, the

fuzzy expert system approach can be adopted for this problem.The outputs of the Kalman filter are considered as inputs to

the fuzzy-expert system to classify the different waveform

disturbances.

The input variables membership functions of the fuzzy expertsystem are shown in Figs. 2 & 3.

For classifying the disturbance waveforms, five fuzzy sets are

chosen for the amplitude (A), the first input of fuzzy-expert,

designated as VSA (very small amplitude), SA (small

amplitude), NA (normal amplitude), LA (large amplitude),and VLA (very large amplitude). The slope (S), the second

input of fuzzy-expert, has three fuzzy sets that are designated

as PS (positive slope), NS (negative slope) and ZS (zero

slope).

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

amplitude (pu)

Degreeofmembership

VSA SA LA VLANA

Fig. 2 Input amplitude membership function

The output membership function is defined by five sets as

shown in Fig. 4. These sets are designated as interruption, sag,normal, swell, and surge. Any output value which is not

belonging to these sets represents the distortion.

The crisp output of the fuzzy system can assume valuesbetween 0.0 and 1.0, where

0.05 Interruption 0.25 Sag

0.5 Normal 0.75 Swell

0.95 Surge.

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

Slope

Degreeofmembership

NSZS PS

Fig. 3 Input slope membership function

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

Fuzzy output

Degreeofmembership

Interruption Normal SurgeSag Swell

Fig. 4 Output membership function

The brief rule sets of fuzzy expert system are below:1. If amplitude is VSA and slope is PS) then output is

INTERRUPTION.

2. If amplitude is VSA and slope is ZS then output is

INTERRUPTION.

3. If amplitude is VSA and slope is NS then output isINTERRUPTION.

4. If amplitude is SA and slope is NS then output is SAG.

5. If amplitude is SA and slope is ZS then output is SAG.6. If amplitude is SA and slope is PS then output is SAG.

7. If amplitude is NA and slope is ZS then output is

NORMAL.

8. If amplitude is NA and slope is NS then output is

NORMAL.9. If amplitude is NA and slope is PS then output is

NORMAL.

10. If amplitude is LA and slope is PS then output is SWELL.11. If amplitude is LA and slope is ZS then output is SWELL.

12. If amplitude is LA and slope is NS then output is SWELL.

13. If amplitude is VLA and slope is PS then output isSURGE.

14. If amplitude is VLA and slope is ZS then output is

SURGE.

15. If amplitude is VLA and slope is NS then output isSURGE.

III. SIMULATION RESULTSThe example taken for the study is a simple power system

consisting of a generator supplying a power network thatcomprises a short transmission line section and three loads

(normal, heavy, and nonlinear loads) at the point of commoncoupling (PCC). The heavy and nonlinear loads are connected

to the system through a circuit breaker as shown in Fig. 5.

Different power quality events have been generated using the

power system simulation tools, MATLAB - Simulink, Fig. 6.


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Fig.5 System configuration of the model used for testing.

The generated signals are mixed with random white noise

of zero mean and the signal to noise ratio (SNR) is 30 db.

Each generated waveform consists of 25 cycles of a voltagewaveform sampled at a rate of 6.4 kHz, which is equal to 128

samples per cycle.

The following case studies are presented to illustrate theaptness of the proposed system:

A

B

C

voltage source A

B

C

A

B

C

three phase short circuit fault

A

B

C

A

B

C

single line to ground fault

A

B

C

A

B

C

Z_source

A

B

C

A

B

C

Z_feeder

A

B

C

+

-

Universal Bridge

voltage.mat

To FileScope

Resistive

load

VabcA

B

C

a

b

c

PCC

A

B

C

Heavy load

emux

A

B

C

a

b

c

C. B1

A

B

C

a

b

c

C. B

A B C

Load

Fig. 6 MATLAB simulation block diagram of the simulated system

Voltage Interruption: an interruption may be seen as aloss of voltage on a power system. Such disturbance describes

a drop of 90-100% of the rated system voltage for duration of

0.5 cycles to 1 min. A waveform of the voltage interruptiongenerated by a 5 cycle three phase short circuit fault at PCC is

shown in Fig. 7(a). Output of the Kalman filter, slope, is

shown in Fig. 7(b). The output of the fuzzy expert system isshown in Fig. 7(c). It is observed that the proposed system can

accurately detect the interruption in the distorted waveform.

The tracking error, which is defined as the difference betweenthe actual and the estimated values of the amplitude voltage, is

found to be less than 0.8%.

Voltage Sag: voltage sage is a decrease of 10-90% of therated system voltage for duration of 0.5 cycles to 1 min. The

sag disturbance is generated by the occurrence of a single lineto ground fault for 5 cycles at the end of the short transmission

line. The results are shown in Fig. 8. The tracking error of

results is less than 0.2%.

Voltage Swell: in the case of voltage swell, there is a riseof 10 to 90% in the voltage magnitude for 0.5 cycles to 1 min.The swell is generated by disconnecting the heavy load for 5

cycles. From the results depicted in Fig. 9, the proposed

system clearly detects and classifies the swell disturbance. The

tracking error is less than 0.4%

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-1

0

1

Time (sec)

W

aveform

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-1

0

1

Time (sec)

Slope

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.5

Fuzzyoutput

Time (sec)

Fig. 7 Voltage interruption: (a) waveform, (b) slope and (c)classification system output

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-1

0

1

Time (sec)

Waveform

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-1

0

1

Time (sec)

Slope

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.25

0.50.60.6

Fuzzyoutput

Time (sec)

Fig. 8 Voltage sag: (a) waveform, (b) slope and (c) classificationsystem output

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-2

0

2

Time (sec)

Waveform

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-2

0

2

Time (sec)

Slope

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50.25

0.5

0.75

11

Fuzzyoutput

Time (sec)

Fig.9 Voltage swell: (a) waveform, (b) slope and (c) classification

system output.

Voltage surge: the surge occurs on disconnecting theheavy load for one-quarter cycle as shown in Fig. 10(a), where

the amplitude is suddenly increased from 1 to 3 p.u. Such a

distorted waveform is tested by the proposed system and the

(a)

(b)

(c)

(a)

(b)

(c)

(a)

(b)

(c)


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results are shown in Fig. 10(b), 10(c) and 10(d). The tracking

error of the magnitude is less than 0.5%.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-1

0

1

2

3

Time (sec)

Waveform

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-1

0

1

Time (sec)

Slo

pe

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

0.5

1

Fuzzyoutput

Time (sec)

Fig. 10 Voltage surge: (a) waveform, (b) slope and (c) classificationsystem output

Voltage distortion: distortion of the voltage waveform isgenerated by connecting the nonlinear load for 5 cycles where

the harmonic is generated. The original distorted waveformand the corresponding Kalman filter and fuzzy expert system

outputs are shown in Fig. 11.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-2

0

2

Time (sec)

W

aveform

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-1

0

1

Time (sec)

Slope

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50.25

0.5

0.75

11

Fuzzyoutput

Time (sec)

Fig. 11 Voltage distortion: (a) waveform, (b) amplitude, (c) slope and

(d) classification system output.

Comparing the results of the proposed system shown fin

Figs. 7 through 11 with the output membership function, Fig.

4, it is observed that each category of the simulated

waveforms is successfully detected and classified.

Another case study is reported to test the overall

performance of the proposed system. In this case, the voltage

waveform at PCC which is captured for fifty cycles and

consists of sag, interruption, swell, and harmonic distortion asshown in Fig. 12 is applied to the proposed system.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Time (sec)

SignalWaveform

Fig. 12 Waveform of the captured voltage.

The voltage sag occurs at t=0.1s for 5 cycles while the outageis started at t=0.3 s and ends at t=0.4 s. The swell is initiated at

t=0.6 s and persists for 5 cycles while the harmonic distortion

is generated at t= 0.8 s for 5 cycles.

The output slope of the Kalman filter is shown in Fig. 13,

while the output of the fuzzy expert system is shown in Fig.14.

Comparing the output waveform of Fig. 14 with the output

membership function, Fig. 4, it is observed that the proposedsystem has successfully detected each disturbance included in

the captured voltage waveform with an average tracking error

of less than 0.5%.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Time (sec)

Slope

Fig. 13 Slope of the captured voltage

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.25

0.5

0.75

11

Fuzzyoutput

Time (sec) Fig. 14 Output of fuzzy-expert system

In addition, the proposed system is computationally simple

in comparison to Fourier linear combiner based approach [9]

and yields classification in short time as it needs two samples

to evaluate the amplitude and slope of the captured voltagewaveform instead of the whole cycle as in [9]. The Kalman

filter, on the other hand, yields more accurate results as the

initial value of the measurement error covariance is notassumed and instead it is accurately extracted with the help of

DWT.

(a)

(b)

(c)

(a)

(b)

(c)


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IV. EXPERIMENTAL RESULTSFig. 15 shows a test waveform that is obtained from the IEEE

Project Group 1159.2 [15]. The sample frequency used is

fs=/15 360 Hz, or 256 samples per 60 Hz cycle. The proposedtechnique is applied on this test waveform.

Kalman filter is used to extract the fundamental frequency

amplitude and its slope as shown in Figs. 16 & 17 from the

practical waveform. The fuzzy expert system output showsthat the test waveform contains a voltage sag disturbance, Fig.18, and there are not harmonic contents in it.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (sec)

Waveform

Fig. 15 The practical captured waveform.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.2

0.4

0.6

0.8

1

Time (sec)

amplitude(pu)

Fig. 16 The amplitude of the practical waveform

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-1.5

-1

-0.5

0

0.5

1

Time (sec)

Slope

Fig. 17 The amplitude slope of the practical waveform

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

0.25

0.5

0.750.75

Fuzzyoutput

Time (sec)

Fig. 18 Fuzzy-expert system output

V. CONCLUSIONSA system based on the DWT, Kalman filter and fuzzy-

expert system is proposed in this paper for classifying power

system disturbances. The DWT is used to extract the noise ofthe captured waveform. The covariance of this noise is

calculated and applied to the Kalman filter with the captured

voltage waveform to improve its performance. The Kalman

filter is then used to estimate the amplitude and the slope ofthe waveform which become the inputs to the fuzzy expertsystem for classification of the waveforms. Several simulation

and experimental tests have been conducted to validate the

performance of the proposed system. The results show that theproposed system performs very well in the detection and

classification of various power system disturbances.

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[3] Angelo Baggini, "Handbook of Power Quality" John Wiley & Sons, 2008

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189 - Wavelet, Kalman Filter and Fuzzy-Expert Combined System for Classifying Power System Disturbances