Wavelet-based signal processing for disturbance classification and measurement

A.M. Gaouda, S.H. Kanoun, M.M.A. Salama and A.Y. Chikhani

Abstract: A systematic method for analysing power system disturbances in the wavelet domain is described. Wavelet domain capabilities in detection, classification and measurements of various power system disturbances are presented. The distortion event is mapped into the wavelet domain and extracted from the measured signal. The duration of the distortion is measured in a noisy environment and its energy and RMS value evaluated. The proposed algorithm is applied to various power system disturbances.

1 Introduction

Automatic data processing, sensitive microprocessors, and power electronic equipment are installed to control and automate assembly lines. However, due to growing economic pressure modern electrical equipment is designed to meet operating limits. This means that equipment manufacturers face a dual responsibility to both desensitise and protect their equipment. This incompatibility issue, between power system disturbances and immunity of equipment, results in a severe impact on the industrial processes. This emphasises the need for a powerful automated monitoring system that can help manufacturers in identifying the gap between various disturbances and equipment susceptibility. The era of deregulation, further- more, pushes electric utilities and customers to identify a baseline for their electric quality levels for complex dynamic systems [ 1-61.

The automatic management of such dynamic systems, controlled by sensitive equipment installed in a polluted electric environment with disturbances that may overlap in time and frequency, requires a widescale power-quality monitoring system with special characteristics. Some of these characteristics are

Fast detection and localisation of disturbances that may overlap in time and frequency in a noisy environment.

Online classification by extracting discriminative, trans- lation invariant features with small dimensionality can represent efficiently the voluminous size of distorted data.

Analysis of different disturbances and measurement of its power quality indices.

Denoising ability and high efficiency in data compres- sion and storing.

0 IEE, 2002 IEE Proceedings online no. 200201 19 DOP 10.1049/ip-gtd:20020 1 19 Paper first received 6th June 2000 and in revised form 3rd October 2001 A.M. Gaouda and M.M.A. Salama are with the Electrical & Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada S.H. Kanoun is with the System Design Engineering, University of Waterloo, Waterloo, Ontario, Canada A.Y. Chikhani is with the Electrical & Computer Engineering, Royal Military College, Kingston, Ontario, Canada

310

A procedure is proposed that will assist in the automated detecting, classifying and measuring of power system disturbances. A new technique that can monitor the variations of RMS value and any further changes in the signal during the distortion event is also presented. The wavelet-domain theoretical basis for RMS value and total harmonic distortion measurements is shown. The distor- tion event s(t) is mapped into the wavelet domain and extracted from the raw data. The duration of the distortion is measured in a noisy environment. The distortion event is classified and its energy and RMS value measured. The proposed algorithm is applied to various simulated disturbances.

2 analysis

Wavelets have been applied in a wide variety of research areas such as signal analysis, image processing, data compression and denoising, and numerical solution of differential equations. Recently, wavelet analysis techniques have been proposed in the literature as a new tool for monitoring and analysing power system disturbances [7-221. The following Section summarises some of the pre- vious work of applying wavelets in the power quality area.

In [7], wavelet multiresolution signal decomposition was applied to detect and localise different power quality problems; the squared wavelet coefficients were used to find a unique feature for different power quality problems that could be used for classification. In [8], wavelet analysis was applied to compress power quality data and the compression ratio achieved was in the range of 3 4 with nomalised mean square errors of the order of lop6 to lop5. In [9], wavelet and Fourier transforms were used to detect the number of notches per cycle and the harmonic content in the voltage to characterise the operational conditions of a converter. The squared wavelet coefficients (WTC1) of the first resolution level are used to detect and count the number of notches per cycle. However, the sampling rate should be very high to detect the notch impulses and therefore the number of coefficients (WTC1) will be very large. Furthemore, the magnitude of the squared WTCl can be affected by the noise content in the signal and other dynamic conditions. In [lo], wavelet and NN techniques were used to classify a one-dimensional signal embedded in normally distributed white noise. These noisy signals were

Review of wavelet application in power quality

IEE Proc.-Gener. Trunsm. Distrib., Vol. 149. No. 3, May 2002

decomposed using both Haar and Daubechies wavelets. A feedfonvard NN was trained on wavelet series coefficients at various scales and the classification accuracy for both wavelet bases compared over multiple scales, several signal-to-noise ratios and varying numbers of training epochs. In [l I], a wavelet transform approach, using Morlet basis, was applied to detect and localise different kinds of power system disturbances. However, it could not easily be used to discriminate among different power quality problems.

Most of the approaches mentioned that dealt with power quality problems did not present a real classification methodology that can be used to classify different power quality problems or to design a practical online automated monitoring system. Most of the work done in the power quality area deals with the power quality problem either from the detection and localisation point of view or from the data compression frame.

3 Mapping into wavelet domain

Assume a finite-length signal with additive distortion of the form

f ( t ) = A t ) + 44 (1) signal pure clklottion

Applying multiresolution analysis, one can decompose the signalflt) at different resolution levels and present it as a series expansion by using a combination of scaling functions qk(t) and wavelet functions tblc(t). This can be mathemati- cally presented as

i- I

where J represents the total number of resolution levels and c,{k) is the set of scaling function coefficients and d,{k) is the set of wavelet function coefficients. For an orthonormal basis the set of expansion coefficients {cJ{k) and d,{ / ) } can be calculated using the inner product

cj-l(k) = ( f ( t ) , P j , k ( t ) ) = C h ( m -2k)c,j(m) (3) in

where h(k) and h,(k) present the scaling and wavelet fLmctions coefficients, respectively. The wavelet function coefficients are related, by orthogonality, to the scaling function coefficients by the following relation:

h l ( k ) = ( - lyh( l - k ) ( 5 )

The input set of the scaling coefficients e,( / ) is obtained from the signal. If the samples of the signalf(t) are above the Nyquist rate, they are good approximations to the scaling coefficients at that scale. This means that no wavelet coefficients are necessary at that scale [23].

In the wavelet domain, using eqns. 3 and 4, the wavelet coefficients that represent the distorted signalflt) at different resolution levels are

where J represents the total number of resolution levels. A set of discriminative, translation-invariant features with small dimensionality that present the energy distribu- tion of .f(t) at different resolution levels can be presented

In a similar way, the wavelet coefficients of a pure signal C,,, can be generated and used as a reference for the purpose of classification and measurements. These coeffi- cients are

cpuvt? = [ C o p l d o p l d l p l * . . . . . . . q - , ) p l ] (10) and their energy distribution can be presented by the norm of the C,,, using eqns. 8 and 9. The wavelet coefficients Cdis, that present the distortion event s(t) are formulated by subtracting eqn. 10 from eqn. 6. Therefore

Cd.st = Csiyriul = Cprire

C d S * '= [Cod ldod I dld I . . . . . . . .d(.- l)d I I (1 1 )

(12)

The proposed feature vector x, that classify the distortion event can be generated by subtracting Epl,,.e from EsigIlu~

This feature vector can be represented mathematically as AE = Esiyrid - Eprm (14)

x0 = [AEco dEddo AEdl . . . . . . d E d ( j - l ) ] (15)

3.1 Distortion detection and localisation Any changes in the pattern of the signal can be detected and localised at the finer resolution levels. As Far as detection and localisation is concerned, the wavelet coefficients of the first finer decomposition level off(t) are normally adequate to detect and localise any disturbance in the signal. These coefficients are

d(J- I ) (k ) = ( f ( t ) , $ ( J - l ) , k ( t ) }

= hl ( m - 2k)c./(m) (16) m

Since the samples of the distorted signalfit) are above the Nyquist rate, the scaling coefficients cJ are presented by the samples of the distorted signalfit). For a pure signal the set of coefficients d(,r-ll(/c) presented in eqn. 16 are equal to zero. Any changes in the signal can be detected and localised in time due to the changes in the magnitude of these coefficients. This property is shown in Fig. 1. An impulsive transient event, Fig. la, is detected and localised owing to the changes in the magnitude of the wavelet coefficients at the first resolution level. However, as the transient event magnitude decreases and the noise level increases, the coefficients that represent the noise will merge with those representing the transient event. Ths will cause a failure in the wavelet detection and localisation property. Fig. 2u shows a harmonic distorted signal where the total harmonic distortion equals 26.6%. The signal is further distorted with a sag to 0.8p.u. for one cycle. If the noise level is small then the first resolution level can be used to detect and localise the sag event as shown in Fig. 2b. However, as the noise level increases, the first resolu- tion level can no longer detect and localise the transient event, Fig. 2c. A new technique relying on noise- level assessment and an approximated version of the

IEE Proc-Gener. Tr~instn. Distrib.. Vol. 149, No. 3, Muy 2002 311

distortion event is proposed to denoise and localise the transient event and to measure its duration Az in a noisy environment.

0010

0.005

ci- 0.0

-0.005

0.01 0

4

3

2

- 3 1

0

-1

-2

I I I - -

I

- - I I I

a

-0.6 I

0 0.0085 0.0170 time, s

b

Impulsive transient event detected and loculised of trunsient Fig. 1 event at first resolution level

3.2 Noise level assessment In multiresolution analysis, as shown in Fig. 3, the first stage will divide the spectrum of distortion into a lowpass and highpass band, resulting in the scaling coefficients and wavelet coefficients at a lower scale qJ- I)&) and , The second stage then divides that lowpass band into another lower lowpass band and a bandpass band. The first stage divides the spectrum into two equal parts. The second stage divides the lower halves into quarters and so on.

The noise is defined as an electrical signal with wideband spectral content lower than 200 kHz superimposed on the distorted signal [3] . Therefore the great part of the noise energy is expected to appear at the highest resolution level (J-1). This means that the energy of the coefficients

at the highest resolution level can give good indication about the energy of the noise superimposed over the signal. For a pure signal

dEd(J-1) = 0 (17) The variation of the AEd(J- with different noise levels on a pure signal is presented in Table 1.

An assessment of the noise level can be determined as the value of goes beyond zero or a certain threshold value.

3.3 Detection and localisation in noisy environment As the noise level increases AE,I(J- 1) > 0 the distortion event can be localised by reconstructing an approximated version of the distorted signal. Ths can be mathematically represented as

F

k k J=o

where F<J and J represents the total number of resolution levels and F represents the subspace index or the highest

1.2

0.6

c 0.0

-0.6

-1.2

h

c

0.050 I I I

Fig. 2 Harmonic distorted signal a One cycle sag to 0.8, the highest resolution level of the distorted signal b Zero noise level c 2.0% noise level

312 IEE Proc,-Gener, Trcmnsm. Distrib., Vol. 149, Nu. 3, May 2002

I -0.2 I I I I I

0.3 I I

-0.3

I _ _ I -0.5 I I

Q++ ::: 0.0

I I n -1.5 3.0

0.0 ..................................................... 1.5 ~ I W

-1.5 I I I 0.46 0.48 0.50 0.52 0.54

time, s

Fig. 3 Multiresolution analysis of distorted signal

Table 1: Coefficient's energy with noise level variation in one-second pure signal

Noise 0.0% 0.25% 0.50% 0.75% 1.0%

A L L - I ) 0.0 0.1521 0.3143 0.4646 0.6345

resolution level to be used to reconstruct s(t) . The value of F depends on the noise-level content and the energy distribution of the distortion event as indicated in eqn, 15. Squaring the distortion event and applying the following thresholds can accomplish further reduction for the existing harmonic:

where

0 = std{s(tj2} (20) Utilising m(t), the start time z , ~ ~ ~ ~ and the end time zCnd of the disturbance event can be localised. The duration AT is measured and used to categorise the disturbance as instantaneous, momentary, or temporary.

AT = 'Tend - Tma (21)

3.4 Distortion classification Relying on Parseval's theorem, the energy of flt) will be partitioned at different resolution levels in different ways depending on the type of the distortion event. Mapping the data of distortion event s(t) into a wavelet domain is the first step in performing the proposed classification process. The distribution of the distortion energy at different resolution levels is computed to generate a set of translation invariant

features with small dimensionality. The term "translation invariant" denotes that the features remain unchanged if the distortion event undergoes a change of position (transla- tion). These features have the property of being able to effectively differentiate between different distortion events. The proposed feature vector x~, can be mathematically represented as

Fig. 4 shows the difference in energy distribution AE at different resolution levels for 25 distorted signals with the indicated power-quality problems.

3.5 Distorlion measurements If the used scaling function and the wavelets form an orthonormal basis, Parseval's theorem relates the energy of the distortion in the signal s(t) to the energy in each of the expansion components and their wavelet coefficients C&. This means that the energy of the distortion W,,,,, can be represented in terms of the expansion coefficients. In terms of the wavelet coefficients the energy of the distortion W,, , is equal to the square of the norm of

IEE Proc.-Genes. Tsrmsni. Dktrih., VoL 149, No. 3. Mny 2002 313

-1.5 ' I I J I I I 0 2 4 6 8 1 0 1 2 1 4

levels

Fig. 4 Distortion ciussijicution in wavelet doinuin

the wavelet coefficients C,,,

(25) 2 WdYt = / I C,Y, I I 2

/ I CdSI 112= J I ( G i s t , Cdist) I

where 1 1 CdjstIl2 is the norm of the distortion coefficients and can be mathematically represented as

(26)

r M M

Therefore the true RMS value of the distortion s(t) can be calculated using the wavelet coefficients as follows:

where AT is the duration of the distortion event measured from the localisation process as mentioned in eqn. 21.

In terms of the wavelet coefficients, the total harmonic distortion (THD) can be computed as follows:

where 1 1 CnUre1l2 is the norm of the pure signal.

3.6 Nonrectangular RMS-variation measurements It has been documented [6] that most distortion RMS variations are rectangular in shape and a single magnitude and duration can accurately characterise them. However, there are other RMS variations with nonrectangular shapes. These variations are difficult to characterise because there is no single magnitude and duration can characterise them, Fig. 5a.

A new wavelet-based procedure to characterise RMS variations is shown in Fig. 6. This procedure can help in assessing the quality of service presented in the distribution systems, the quality of the mitigation devices, and the characteristics of'any load during RMS variations. It can also give important information about any new variations of the distortion within its period. This information may help in finding the source of the disturbance. The proposed

h d l 2.0 I I

I .o - p 0.0

-1.0

-2.0 0.0 0.1 0.2 0.3 0.4

a

2.0

1 .o = 0.0

-1 .o -2.0

h

%.

b

Q-o:I -0.15 0.00 HHHBBHHB 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

time, s C

resolution level, L, d

Fig. 5 RMS variation monitoring

314 IEE Proc-Gene?. Txinsni. Distrih.. Vol. 149, No. 3, Muy 2002

I input f ( t )

;m;; T = -1

I PkNEw = PkNEW + T * Pk

Fig. 6 RMS vnriution monitoring Jow chart

procedure is summarised in the following points and in Fig. 6:

Any changes in the pattern of the signal can be detected and localised at the finer resolution levels, as presented in Sections 3.1 and 3.4. The set of coefficients d(Jp,)(k) presented in eqn. 16 is used to monitor the number of changes in the signal during the selected window size.

The distorted signal is segmented into window frames with respect to a fixed time interval as shown in Fig. 5b.

For each frame, find the wavelet coefficients C and Cdi,vt, where

C(ti.st = C - CR,,~ (30)

and CxeJ is a reference wavelet coefficients computed from C,IlVt?

CRe.f Pknew * c p w e (31)

where Pk,,, is the peak value of the distortion event. Its initial value is selected to be equal to 1p.u for a pure signal.

Using C(zisr, the new RMS,(,) and its peak value Pk of the distorted signal is estimated.

Use the energy measure dEnel(Lf) of the resolution level Lf, that covers the power frequency band, to monitor the direction of variation in the RAIS.y(rl of the distortion event, as shown in Fig. 5d, where

d E ~ , r , ( L f ) > 0 @ increasing in RMS value d E ~ ~ f ( L f ) < 0 e decreasing in RMS value d E ~ , f ( L f ) = 0 H no change in RMS value

The Pk,?,,” value is updated to be used for monitoring the new variation in RMS value, if it exists in the second window frame

and

Use the proposed feature vector eqn. 15 to classify the type of distortion in the signal.

4 Application and results

4.7 Detection and localisation in a noisy environment The proposed method is applied to detect, localise and estimate the duration of the following power system disturbances with different noise levels.

4. 7 . 7 Capacitor-switching phenomenon: The sig- nalJ(t), Fig. 7u and its zoomed version Fig. 7b is simulated with the capacitor-switching distortion. The actual start time of the distortion is 0.4901 s and the end time is 0.4926 s. The proposed algorithm in Section 2.3 is used to estimate the time information of the distortion. The distortion event

1.2

0.6 ,--. 2 0.0

-0.6

- 1 7 0.47 0.51

1 .o

0.6 E

0.2

-0.05 -0.2 0.4888 0.4909 0.4930 0.4888 0.4909 0.4930

time, s time, s d e

Fig. 7 menon in noisy environment

Detection and localisution of’ cupucitor-s~vitcl~in~ pheno-

IEE Proc.-Gener. Trunsn. Distrib., Vol. 149, No. 3, May 2002 315

Table2: Estimated start and end times of a capacitor- switching phenomenon with noise level between 0-1.2%

Table 3: Estimated RMS value and start and end times of sag phenomena in noisy environment

~ ~ ~ ~ ~~ ~ -

Noise Start time Start error End time End error level [SI [SI %

% ~ ~ ~ ~ ~~ .~ ~

0.0% 0.4901 0.0 0.4919 0.1239

0.5% 0.4901 0.0 0.4919 0.1239

1.0% 0.4901 0.0 0.4919 0.1239

1.1% 0.4901 0.0 0.8604 74.671

1.2% 0.1838 62.490 0.4919 72.961

s(t) is synthesised using the wavelet coefficients C& as shown in Fig. 7c. The threshold measure eqn. 20 is applied on [s(t)I2 and m(t) is constructed to estimate the time information of the distortion, Figs. 7d and 7e. Table 2 presents the estimated start and end times of the capacitor- switching phenomenon with noise-level variation from 0 to 1.2%. It can be seen that the estimated time error is increased considerably as the noise level magnitude goes beyond 1.0%. However, higher values of noise level larger than 1.0% is not normally found in power systems [3].

4.1.2 Sag in noisy environment: The same techni- que is applied for detecting and localisation a one-cycle simulated sag phenomenon, Fig. Xu. The simulated signal is further distorted with harmonics and has a high noise level. The end time of the distortion is 0.4917s and the start time is 0.5083s. Due to the high 1.0% noise level the first resolution level D,, Fig. 8b, can no longer detect and localise the distortion event. The distortion event s(t) is synthesised

1.2 I I I

0.6

h p 0.0

-0.6

-1.2 ' I I I J

0.3 0.4 0.5 0.6 0.7 a

0.025

Q- 0.0

-0.025 -0.2

U 0.3 0.5 0.7

-0.050 -0.4 0.3 0.5 0.7

b C

0.10 -1

1 .o

i3' 0.6 E -

0.2

-0.2

a, 0.05

Y

-0.05 0.48 0.50 0.52 0.48 0.50 0.52

time, s time, s d e

Fig. 8 environment

Detection and localisation of sag phenomenon in noisy

Noise Derived Error Derived Error Derived Error level sag % start ( s ) % end (s) %

(RMS)

0.00% 0.1798 0.0150 0.4921 0.0745 0.5082 0.0240

0.25% 0.1814 0.0240 0.4921 0.0745 0.5081 0.0480

0.50% 0.1840 0.0384 0.4921 0.0745 0.5082 0.0240

0.75% 0.1895 0.0706 0.4921 0.0745 0.5082 0.0240

1.00% 0.1954 0.1014 0.4921 0.0745 0.5082 0.0240

1.25% 0.2058 0.1622 0.4922 0.0993 0.5082 0.0240

1.50% 0.2179 0.2331 0.4921 0.0745 0.5081 0.0480

1.75% 0.2284 0.2926 0.4921 0.0745 0.5081 0.0480

2.00% 0.2382 0.3400 0.4922 0.0993 0.5082 0.0240

ignoring the high resolution level F= 9 and J= 13 for denoising, Fig. 8c. The threshold measure (eqn. 20) is applied on [s(t)I2 and m(t) is constructed to estimate the time information of the distortion, Figs. Sd and Se. Table 3 presents the estimated RMS value and start and end times of a sag phenomenon with noise-level variation from 0 to 2.0%.

4.2 Feature extraction of transient event The proposed feature extraction technique is applied on the distorted signal At) in Fig. 9a (capacitor switching). The

I I I I I

-2 ' I I I I I a

0.250 I I I I I i

0.125

a- -0.125

I -0.250 ' I I I I I

0 0.01 0.02 0.03 0.04 0.05

b

60

50

40

30 Lu"

20

10

0 C

2o - -1 0

0 2 4 6 8 1 0 1 2 1 4 resolution levels

d Fig. 9 Feature extraction and classgcation for capacitor switching phenomena

316 IEE Prac.-Gener. Trunsm. Distrib., Val. 149, No. 3, Muy 2002

Table 4 Typical characteristics of transient phenomena in power systems

A-Impulsive Typical Typical Typical transient spectral duration magnitude

1 -nanosecond 5ns rise i 5 0 n s

2-microsecond 1 ps rise 50 ns-I ms

3-m illisecond 0.1 ms rise < I ms 6-oscillatory Transient

I-Low frequency i 5 kHz 0.340 s &4 PU

2-Medium freq. 5-500 kHz 20 ps 0-8 P U 3-High frequency 0.5-5 MHz 5 ~ s 0-4 pu

Part of Table 2 IEEE Std. 1159-1995

energy distribution for both the distorted signal (dashed line) and pure one (solid line) is shown in Fig. 9c. The extracted feature vector for At) is shown in Fig. 9d. The distorted signal is sampled at 165 kHz (8266 sampling points) and mapped into small-size feature vector (13 numbers). This feature vector extracts the energy of the distortion event and distributes it on different resolution levels. Fig. 9d shows that most of the distortion energy is concentrated on the seventh resolution level (645-1289 Hz). The time information of ths distortion event is measured from the first resolution level and found to be 7ms as shown in Fig. 9b. These results, resolution level = 7, frequency band = 645-1289 Hz and duration = 7 ms, are compared with the categories of electromagnetic phenom- ena presented by IEEE 1159 and shown in Table 4. The distortion event is then classified as oscillatory transient with low-frequency content.

4 . 3 Nonrectangular RMS-variation measurements A 21-cycle distorted signal A t ) is simulated. Ths signal undergoes six variations in its magnitude and duration. The distorted signal is segmented into three-cycle window frames. The feature extracted from each window frame is used to classify the type of distortion. The energy distribution A E(Lf) is used to classify the distortion event as

AE(Lf) < 0 d E ( L f ) > O d E ( L f ) = 0 H Esipa/(Lf) = Efi,,.e(Lf) H pure signal

The proposed technique, Section 3.6, is used to monitor the RMS variation during the distortion event and A E x , ~ L ~ ) is used to monitor the direction of the variation !increased or decreased).

Fig. 10 shows the process of classifying and monitoring the RMS variations during any distortion event. Fig. 10a shows the distorted signal contaminated with the RMS variations that are shown in Table 5. Fig. 10h shows a different window frame; each frame presents three cycles of the distorted signal. The time localisation property for different variations is extracted from the detail version of the distorted signal D1 for each frame as shown in Fig. 1Oc. As the noise level increases, the proposed algorithm in Section 3.3 is used to localise the distortion event. Fig. 10d shows the variation of distorted signal energy distribution AE with respect to the power-frequency resolution level Lf The four lines in Fig. 1Od are

Esignal ( L f ) < E/+,r (Lf) e sag &iqna/(Lj ' ) >Efire(Lf) % swell

EyiG,nol (Lr> soiled line on the top

EPuFe (Lf) dotted line on the top

2 1 I

0.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 a

L

0.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 b

-0.1 -~~~~~~~ 0.0 0.05 0.10 0.15 time, s 0.20 0.25 0.30 0.35

C

10 11 12 1310 11 12 1310 11 12 1310 11 12 1310 11 12 1310 11 12 13 10 11 12 13 resolutional levels

d

Fig. 10 RMS variation monitoring

IEE Proc-Gener. Trunsm. Distrib,, Vol. 149, No. 3, May 2002 317

Table 5: Nonrectangular RMS-variation measurements

Frame Actual variation Estimated variation

Mag. Times (s) Mag. Time (s) (peak) (peak)

1 1.3500 0.0296 1.361 4 0.0296

2 0.8775 0.0864 0.8287 0.0864

3 0.1316 0.1391 0.1192 0.1391

4 0.5265 0.1599 0.5429 0.1600

5 0.8424 0.2180 0.8588 0.2184

6 1 .oooo 0.2702 1.0068 0.2703

7 1 .oooo 0.3000 0.9966 0.3010

dE(Lf) dashed line on the top

A&,&) solid line on the bottom

The first frame in Fig. lOdshows that the signal dE(L1) and dERe&) are coincident with each other. dE(Lf) is greater than zero which represents a swell phenomenon and

(Lj) also greater than zero which represents an increase in the RMS value. The second frame shows dERef(Lf) is less than zero, representing a reduction in the RMS of the signal and dE(Lf) is greater than zero, representing a swell phenomenon. The third frame repre- sents a reduction in RMS value and sag phenomenon.

The proposed technique is implemented in different sets of simulated data. The results of applying the technique to the distorted signal, shown in Fig. loa, are presented in Table 5.

5 Conclusions

A wavelet-based procedure has been presented that assists in automated detecting, classifying and measuring various power system disturbances. The localisation property of the wavelet transform is used to detect and measure the distortion duration in a noisy environment. The RMS value of the distortion event magnitude is measured using wavelet coefficients. The variations of the RMS value during the distortion event are also monitored and measured. The following points are summarised:

Any distortion in the signal can be detected and localised using wavelet coefficients at the higher resolution level (eqn. 16). However, as the noise level increases and the transient-event magnitude decreases, the coefficients that represent the noise will merge with those that represent the distortion, and the wavelet detection and localisation property will no longer be valid at this resolution level.

An assessment of the noise level can be determined by computing the energy of the coefficients at the highest resolution level (eqn. 17).

As the noise levels increases, the distortion event can be localised by reconstructing an approximated version of the distortion event (eqn. 18).

The energy of the distortion event at different resolution levels is used as a feature vector that can classify different disturbances (eqn. 22). These discriminative, translation- invariant features with small dimensionality can be used to classify different power-quality problems that overlap in time and frequency.

The wavelet coefficients of the distortion event can be used to measure the RMS value and the THD% of the distorted signal (eqns. 28 and 29).

A new wavelet-based procedure to characterise RMS variations is presented in Section 3.6. This procedure can help in assessing the quality of service presented in the distribution systems, the quality of the mitigation devices, and the characteristic of the load during RMS variation. Utilising this procedure, a clear picture of any further changes in the harmonic distortion, noise level, or RMS variations can be detected, localised, classified, and quantified inside the distortion event.

6

I

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

References

SABIN, D., and SUNDARAM, A,: ‘Quality enhances reliability’, IEEE Spectr,, 33, (2) 1996, pp. 3441 DOUGLAS, J.: ‘Solving problems of power quality’, EPRI J., Dec. 1993, 18, (8), pp. 6-15 DUGAN, R.C., MCGRANAGHAN, M.F., and BEATY, H.W.: ‘Electric power systems quality’, (McCraw-Hill, 1996) KEY, T.S.: ‘Diagnosing power quality-relaled computer problems.’, IEEE Trans, Ind Appl, July/August 1979, 15, (4), pp. 381-393 HEYDT, G.T., and JEWELL, W.T.: ‘Pitfalls of electric power quality indices’, IEEE Trans. Power Deliv., Apr. 1998, 13, (2), pp. 57&578 BROOKS, D.L., DUGAN, R.C., WACLAWIAK, M., and SUN- DARAM, A,: ‘Indices for assessing utility distribution system RMS variations’, IEEE Trans. Power Deliv., Jan. 1998, 13, (l), pp. 254259 SANTOSO, S., POWERS, E.J., GRADY, W.M., and HOFMANN, P.: ‘Power quality assessment via wavelet transform analysis’, IEEE Trans, Power Deliu., Apr. 1996, 11, (2), pp. 924930 SANTOSO, S., POWERS, E.J., and GRADY, W.M.: ‘Power quality disturbance data compression using wavelet transform methods’, IEEE Truns. Power Deliv., July 1997, 12, (3), pp. 125M257 SANTOSO, S., GRADY, W.M., POWERS, E.J., LAMOREE, J., and BHATT, S.C.: ‘Characterization of distribution power quality events with Fourier and wavelet transforms’, IEEE Truns. Power Deliv., Jan. 2000, 15, (l), pp. 247-254 JOHNSON, C.M., PAGE, E.W., and TAGLIARINI, G.A.: ‘Signal classification using wavelets and neural networks’. Proceedings of SPIE international symposium on Wavelet applications 111, Orlando, FL April 1996, pp. 202-207 HUANG, S.J., HSIEH, C.T., and HUANG, C.L.: ‘Application of Morlet Wavelets to supervise power system disturbances’, IEEE Trans. Power Deliv., Jan. 1999, 14, (I), pp. 235-243 ROBERTSON, D.C., CAMPS, O.I., MAYER, J.S., and GISH, W.B.: ’Wavelets and electromagnetic power system transients’, IEEE Trans. Power Deliu., April 1996, 11, (2), pp. 1050-1058 GAOUDA, A.M., SALAMA, M., SULTAN, M., and CHIKHANI, A,: ‘Power quality detection and classification using wavelet-multi- resolution signal decomposition’, IEEE Truns Power Deliv., Oct. 1999, 14, (4), pp. 1469-1476 ANGRISANI, L., DAPONTE, P., D’APUZZO, M., and TESTA, A,: ‘A measurement method based on the wavelet transform for power quality analysis’, IEEE Trans. Poiver Deliu,, October 1998, 13, (4), pp. 990-998 YOON, W.K., and DEVANEY, M.J.: ‘Power measurement using the wavelet transform’, IEEE Trans. Instrum. Meas., Oct. 1998, 47, (5),

GAOUDA, A.M., SALAMA, M., and SULTAN, M.: ‘Automated recognition system for classifying and quantifying the electric power quality’. Proceedings of the 8th international conference on Harmonics and quality of power, Athens, Greece , Oct. 1998, pp. 244248 PILLAY, P., and BHATTACHARJEE, A,: ‘Application of wavelets to model short-term power system disturbances’, IEEE Tram Power

WILKINSON, W.A., and COX, M.D.: ‘Discrete wavelet analysis of power system transients’, IEEE Trans. Power Syst., Nov. 1996, 11,

LITTLER, T.B., and MORROW, D.J.: ‘Wavelets for the analysis and coinpression of power system disturbances’, IEEE Trans, Power Deliv., April 1999, 14, (2), pp. 358-364 HEYDT. G.T.. and GALLI. A.W.: ‘Transient Dower aualitv

pp. 1205-1209

Sy~t . , NOV. 1996, 11, (4), pp. 2031-2037

(4), pp. 2038-2044

problems analyzed using wavelets’, IEEE Truns, Po& Deliv., April

MELIOPOULOS, A.P.S., and LEE, C.-H.: ‘Wavelet based transient analysis’, Proceedinqs of North American Power Symposium, Oct.

1997, 12, (2), pp. 908-915

. - . - 1997, pp. 339-346 CHAARI, O., MEUNIER, M., and BROUAYE, F.: ‘Wavelets: A new tool for the resonant grounding power distribution system relaying’, IEEE Trans. Power Deliu., July 1996, 11, (3), pp. 1301-1308 MAGNAGO. F.H., and ABUR, A,: ‘Fault location using traveling waves and wavelet transform’, Proceedings of North American Power Symposium Oct. 1997, pp. 332-338 BURRUS, S.C., GOPINATH, R.A., and GUO, H.: ‘Introduction to wavelets and wavelet transform’ (Prentice Hall, New Jersey, 1997)

318 IEE Proc.-Gener. Trcinsm. Distrih., Vol. 149, No. 3, May 2002