Analysis of Power Quality (PQ) Signals by Continuous Wavelet Transform

Malabika Basu, Member IEEE Biswajit Basu, Member IEEE School of Control Systems and Electrical Engineering School of Engineering Dublin Institute of Technology Trinity College Dublin Kevin Street, Dublin 8 Dublin 2 Ireland Ireland

Abstract-This paper presents application of continuous wavelet transform to identify power system transients and disturbances. A mother wavelet basis function (Littlewood-Paley (L-P)) with dyadic non-overlapping frequency bands has been used. A few power signals with power quality (PQ) disturbances have been analyzed to show the effectiveness of the proposed technique. The purpose of the paper is to highlight an alternative way of PQ signal analysis, which enables to identify the duration of disturbance accurately. Classification of various power quality disturbances is also possible through this time-frequency based wavelet analysis.

Keywords - power quality, voltage distortion, spike,saturation, flat-top, wavelet analysis, L-P basis

I. INTRODUCTION

Power quality (PQ) issues are gaining increasing importance for several reasons. Due to proliferation of semi-conductor device based applications and/or equipment, in the distribution systems, both utility and consumers are affected by wide-range of unknown harmonics generated by high-tech customers throughout the network. Quality of utility services has become more critical due to presence of non-linear voltage sensitive loads. [1],[2] Most of the renewable energy integration to the grid is through power electronics based equipment, so the PQ issues are matters of concern there as well.

Detecting PQ disturbance and finding the root cause of such an event would be an essential part in taking control over unwanted PQ events. Simultaneous frequency and temporal information would be very useful in curbing transient phenomena which can have cascading catastrophic failures in the network [13].Several techniques have been envisaged to counteract different unwanted PQ disturbances. The necessity of classification of PQ signals has been felt and it has been widely investigated [4]- [7], [14]- [16]. The identification of sources of disturbances holds an important part in curbing PQ problems from propagating further in the network and causing cascading problems. Therefore, monitoring of PQ signals forms an essential part of taking suitable counter-measures, as well as in identifying the probable cause of concern. For some incidents, the

apparent disturbance signals may seem to be similar, but their causes might be different and they may require different actions to be taken subsequently. For example, it would not be desirable that a closure of capacitor switching activates a Static Transfer Switch (STS) [3], while a voltage disturbance due to a remote fault may require a STS to operate. There are other incident events, e.g., a voltage sag/swell, which may require a Dynamic Voltage Restorer (DVR) to be operated to compensate the disturbance to avoid interruption to precision manufacturing industries such as semiconductors, chemicals, medicines etc.Thus rapid detection of disturbances with identification of types of events is essential for PQ enhancement. Poor PQ may cause problems for the affected loads, such as malfunctions, instabilities, and short lifetime. Continuous vigilance of PQ signals has also emerged as an important area, which helps in online monitoring and further post-analysis of any unwanted eventuality.

Poor PQ is often caused by power line disturbances such as impulses, notches, glitches, momentary interruptions, over and under voltages, and harmonic distortions. In order to determine the causes and sources of the disturbances, it is not only required to detect and localize those disturbances but also identify and classify their types and duration of disturbances. Manual procedures for determining the disturbances are more expensive and inefficient in nature. The current state of the art with regard to detection of PQ disturbances is based on point-to-point comparison of adjacent cycles. This technique suffers from the limitation that disturbances appearing periodically such as flat-topped and load controlled wave shape may not be detected. The approach of neural networks (NN) has been also used by [4] for the purpose of disturbance detection. However, the approach based on NN is more specific as a particular type of NN is required to detect a particular kind of disturbance, and hence lacks generality in application. Another ruled based S-transform technique has been reported [14] to classify PQ disturbances.

The use of continuous wavelet transform (CWT) to analyze non-stationary harmonic distortion has been proposed by [5],[6]. Further, studies on PQ assessment by using a dyadic orthonormal wavelet were carried out by [7]. Wavelets were used for

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analyzing Electromagnetic transients by [8]. Otherresearches on PQ detection and problems usingwavelets include [3]. Corresponding to each scale thewavelet transform coefficients relate to thecontribution of the signal at an instant of time and to that scale. This feature could be used to identifydisturbances in a signal like sag and swell, transientelectromagnetic disturbance, harmonic distortion etc.Most of the researches carried so far have used wavelet basis function, which have overlappingfrequency bands [15].

In this paper a wavelet basis function that has non-overlapping frequency band has been used. Thiswould have the advantage of detecting disturbancescorresponding to certain frequency bands, which areunaffected by the contributions from other bands. Thewavelet basis function used is conventionally calledLittlewoodPaley (L-P) basis function. This paperproposes techniques to detect and localize actual PQ disturbances measured by power line monitoringdevices using L-P basis function. A scheme forclassifying different types of PQ disturbances is alsodiscussed using the wavelet analysis (WA) basedtime-frequency approach. A comparative analysis ofthe signals with FFT has also been reported tohighlight the strengths of the wavelet analysis and theadditional features it provides.

II. BASIC THEORY OF CONTINUOUS WAVELETTRANSFORM

Let f(t) be a zero mean signal. The wavelettransform, W\f(a, b) of this signal and thecorresponding inversion relationship are given as follows [9]

dta

bttfa

bafW f

f

\\ )(

1),(2

1 (1)

and

dadbtbafWaC

tf ba )(),(1

21)( ,2 \S \\

f

f

f

f

(2)

with

dww

wC

f

f

2

)(\\ (3)

and

f

f

dtetw iwt)(21)( \S

\ (4)

is the Fourier transform of the function \(t). In Eq.(1),

the function

abt

a\

21

1 , often denoted by

\a,b(t) (as in Eq.(2)) is obtained by translating thefunction, \(t), to the time instant t=b and thendilating by a factor of a. The function \(t) is calledthe mother wavelet. The parameter, b, has the

significance of localizing the basis function at t=band its neighbourhood. The parameter, a, captures thecontribution of f(t) to the frequency bandcorresponding to the Fourier transform of\a,b(t)( i.e., iwbe)aw(a \

). Thus, W\f(a,b)contributes to the function, f(t), in the neighbourhoodof t=b and in the frequency band corresponding to thedilation factor a. This time-frequency localizationfeature of wavelet transform will be used fordetecting PQ disturbances.A. Littlewood-Paley (L-P) Wavelet Basis Function

The basis function used as mother wavelet in thisstudy is described by

ttSintSint SVS

VS\

.

11)( (5)

The Fourier domain characteristics of mother wavelet

is given by

otherwise0,,

121)( VSS

SV\ dd

ww

(6)In particular, a value of V = 2 leads to L-P basis

and harmonic wavelet proposed and used by [10][11].The use of CWT provides the flexibility of choosingthe scaling parameters to adjust the frequency bandsas desired. A value of V = 2 has been used in thispaper. The parameters a and b are continuous forCWT. For numerical computation of waveletcoefficients (WC) these parameters may be discretized for numerical calculation as, aj = Vj andbi = (i-1).'b, where, i, j I . Note that thisdiscretization leads to a discrete parameter wavelettransform [12] of the CWT. Suitable choice ofparameters V and 'b will lead to orthogonal basis.

Unlike Short Term Fourier Transform (STFT), theanalysis is not window dependent and numericallyefficient. In PQ monitoring exact reconstruction ofsignals are not necessary, hence discrete wavelet analysis may not be used though discrete wavelet hasbeen one of the popular basis used so far. However,the LP basis function analyses a given signal to extract local frequency information over a band offrequencies, whereas for PQ analysis the signals will normally contain the fundamental and combination of discrete sinusoids. Nevertheless, the continuous LPwavelet basis can be designed by adjusting thescaling parameters. In this way for the lower orderharmonics only one of the harmonics will lie in anygiven frequency band corresponding to a scale of LP basis. This makes L-P basis function a competentcandidate for analyzing harmonic signals.

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III. DETECTION AND CHARACTERIZATION OF SEVERAL PQ DISTURBANCES BASED ON CWT

ANALYSIS

B. Characterization of Voltage Spike

Figure 3a shows a voltage waveform signal with 2sharp spikes over very short duration in the 3rd and 4thcycle respectively. WC plotted in Figure 3b ischaracterized by two sharp spikes, corresponding to the location of input spikes. Rest of the coefficientsare quite low. On comparing the results of FFTanalysis on the signal with spike, it is interesting to note that FFT cannot detect the presence of highfrequency spikes at all, as their energy content is verylow, but WC could extract out the phenomenon veryaccurately.

To validate the proposed detection and localizationtechnique, some simulated PQ disturbances in voltagesignal of rms magnitude of 230V and fundamentalfrequency 50 Hz are considered which would betypically present in practical situation. Thesedisturbances were simulated to represent thefollowing casesx Spikes /high frequency distortions in the voltage

waveform, due to other network switching eventsx Saturation of voltage occurring due to voltage

swell

The magnitude of the CWT is calculatedconsidering a few frequency bands. Since thefundamental frequency considered in all the cases is 50 Hz, the fundamental frequency band for themother wavelet is considered as 45-90 Hz (1st band).As a dyadic wavelet has been used, the six higherbands correspond to frequency ranges

90-180 Hz (2nd band),180-360 Hz (3rd band),360-720 Hz (4th band),720-1440 Hz (5th band),1440-2880 Hz (6th band)and 2880-5760 Hz (7th band).WC are calculated by discretising the parameter b

at an interval of, 'b = 39.0625Psec (0.02/512). Thecalculated WC are used to identify and detectdifferent kinds of disturbances. WC with high valuesindicates PQ disturbances, while smaller values areindicative of electrical noise.

A. Characterization of High Frequency DistortionFigure 1a. Voltage signal with high frequency distortion

Figure 1b. Wavelet coefficients of the 6th band Figure 1a shows five cycles of power signals withfundamental frequency 50 Hz. In the 3rd and 4th cyclethe nature of the wave shape have been distorted dueto high frequency decaying noise. The noise signal, S(t) has been simulated by the following Eq. 7 in theappropriate small interval (0.004 sec) 50sin(30.2S50t).exp(-20t) (7) The WC corresponding to band 6 captures this as shown in Figure 1b. WC have been found to be uniformly high over these phases where thedistortions are present.Figure 2 shows FFT of the voltage signal with highfrequency distortion. A high frequency harmonic(1500Hz) has been detected in the FFT. However, theexact time of occurrence is revealed only by WCwhich could be useful in finding out the cause of suchhigh frequency distortion. This is an added advantageof using wavelet analysis as compared to the Fourierbased analysis.

Figure 2. FFT of signal with high frequency distortion

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Figure 3a. Voltage signal with high frequency spike Figure 3b. Wavelet coefficients of the 6th band

C. Superimposed Power Quality Disturbance

In the previous section, classification and identification of some of the common PQ signalshave been discussed. In this section simultaneousoccurrence of PQ disturbances would be analyzed.One of the most common examples could be thesaturated voltage flat-top condition occurring due tounwanted rise or swell in voltage, as shown in Figure4a, where the voltage top saturates at 345 V. Thesituation has been simulated, when the swell in voltage starts at t = 0.022 sec, and continues till t = 0.078 sec. Figure 4b plots the wavelet coefficients ofband 6. They clearly identify the duration of voltageswell, as well as clearly identify the duration of flat-top condition separately.It is interesting to note that FFT analysis is clueless ofthis complicated phenomenon (shown in Figure 5). Itcan only detect the prominent presence of 3rd and 5thharmonics, but cannot yield any further information.

D. Discussion on the Results of CWT Analysis

From the results in the previous section it is found thatthe short duration PQ disturbances excited the frequency range of 6th band ( in this case 1440- 2880 Hz), where, theWT coefficients get significantly higher than coefficients of an ideal fundamental sinusoidal signal of 50 Hz. Butremarkably, the signatures of concentration of the WTcoefficients are found to be prominently distinct accordingto the nature of the disturbance. This feature can be utilized

to further classify the PQ disturbances and automaticidentification of various PQ events.

Figure 4a. Voltage signal with swell and flat-topFigure 4b. Wavelet coefficients of the 6th band

Figure 5. FFT of signal shown in Figure 4a

IV. CONCLUSION

An efficient yet simple technique using CWT hasbeen developed to detect and characterize PQ disturbances. This approach very accurately locatesspike, harmonic distortion and voltage saturationtemporally. Test has been performed on identifyingsuperimposed disturbance detection, where theduration of voltage swell has been identifiedaccurately and within this time of disturbance, the

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second disturbance of voltage flat-top has been detected clearly. The concentration signature of the WT at the high frequency band where, the short duration transient frequencies flock together ( in the present case, 6th band, with a frequency range (1440 2880 Hz), are found to be very distinct from each other according to the nature of the disturbance. This would help in classifying various PQ events based on some pattern recognition technique.

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