pq event detection using joint 2d-wavelet subspaces

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 1

Power Quality Event Detection using Joint2D-Wavelet Subspaces

Dogan Gokhan Ece, Member IEEE, Omer Nezih Gerek, Member IEEE,

Abstract— In this work, we present a novel 2D represen-tation of power system waveforms for the automatic analy-sis and detection of transient events. The representation iscomposed of a matrix whose rows are formed by time seg-ments of digital waveforms. By the appropriate selectionof the time segment length, the 2D data exhibits wave–likeimage shapes. The general shape is immediately disturbedwhenever a power quality transient event occurs. We pro-pose the use of two dimensional discrete wavelet transforms(2D–DWT) to detect these disturbances. It has been ob-served that, after omitting the approximation space signalsof the wavelet transform and denoising the detail space sig-nals, the inverse 2D–DWT provides good detection and lo-calization results, even for cases where conventional meth-ods fail. Examples are presented.

Keywords—Power quality, event detection, 2–D wavelet de-

composition

I. Introduction

Many events and disturbances in the power system volt-age or current waveforms can be detected by just exam-ining the waveforms with an expert eye. Automatic eventdetection is a research area which attempts to generaterules and tools that build up a system performing the wayexperts make the detection. The state-of-the-art tools uti-lizing wavelet decomposition may be used to develop suchwaveform processing systems. To detect, solve, and pre-vent the power quality (PQ) problems, an efficient postevent processing of PQ data is required. A major postprocessing issue is feature extraction for detection, local-ization, and classification of PQ events. For this issue,wavelet analysis has proven to be a very strong and efficienttool. Wavelet analysis is capable of revealing features ofdata that other analysis tools could miss, including trends,breakdown points, discontinuities, and self–similarity. Thisissue has been well researched, and a survey in [2] cites afair span of literature. Conventionally the event data asoscillographic waves of current or voltage is first captured,then classical wavelet based or adaptive transforms are ap-plied. Finally the output is analyzed by thresholding orother statistical techniques [3]-[8].

In this paper, we present a new two-dimensional (2D)analysis of the power quality data that enables efficientevent detection and localization. The approach relies on anovel 2D representation of the waveform data and its 2Dwavelet analysis. We first develop the method to convertthe waveform data into 2D. Next, the 2D discrete wavelettransform (2D-DWT) is proposed as the tool to apply on

This work is supported by Anadolu University Research Fund Un-der Contract: 000212. Authors are with Anadolu University, Schoolof Engineering and Architecture, Electrical and Electronics Engineer-ing Department, Eskisehir, TURKEY

the 2D data. Due to the new representation, the 2D-DWTautomatically supplies the regular 1D wavelet subspaces,as well as subspaces which exploit other features that canonly be observed in the 2D representation. To test the de-tection performance, we used voltage waveforms from reallife power quality events captured at 20 kHz from an ex-perimental system. Experimental system is composed of athree-phase wye-connected 380 V, 50 Hz, 25 kVA, 5-wiresupply loaded with RL load banks and three-phase induc-tion motors coupled with varying mechanical loads. Systemalso includes adjustable speed drives controlling the induc-tion motors for studying load generated harmonics. Datais captured using National Instruments PCI–MIO–16E–4A/D unit and LabVIEW 6.0 virtual instrument software.The use of computer generated data is avoided. Inherently,the 2D implementation has all the analysis benefits of theregular DWT that were presented in the literature. Fur-thermore, the new approach is observed to have advantagesin detection of PQ events that may not result in necessarilyabrupt waveform discontinuities, but rather in slow wave-form variations such as sags, swells and frequency fluctua-tions that may not always be detected using 1D-DWT.

II. 2D Representation of Event Data

Waveform representation and enhancement sometimesimprove the detectability of the features that can be missedwhen using the oscillographic data in its original form. Therepresentation change from 1D voltage or current waveformto 2D image form is new in the area of power quality stud-ies [1]. There is a great potential in analyzing the PQ eventdata in 2D because of the vast amount of research in thefield of image processing and image pattern recognition.

The proposed 2D representation consists of a matrixwhose rows correspond to non-overlapping segments of thewaveform data. In this way, the data can be consideredas an image or a 2D surface. The new representation hasmore operational flexibility because of the available imageprocessing tools in the literature. As a practical implemen-tation detail, the time segments, which are placed in therows, should have a duration of an integer multiple of thedata period. In this way, the cyclo-stationary behaviourof the waveform is exploited well, and the image surfaceresembles water waves. The generation of a 2D image fromthe 1D data can be graphically illustrated as in Figure 1. InFigure fig2(a), the 2D image generated from a real life PQevent is shown using the surface plot. The grayscale imagecorresponding to the same data is shown in Figure 2(b).

The 2D representation has some significant benefits overthe regular 1D signal representation. If an event in the


Fig. 1. 2D matrix (or image) generation from 1D data.

50 100 150 200 250 300 350 400

50

100

150

200

250

300

350

400

450

(a) (b)

Fig. 2. 2D matrix generated from an example real life transient: (a)in surface form, (b) in grayscale.

power system produces a change in the magnitude of thevoltage or current waveform (such as a sag, swell, andswitching–on/off loads), the waveform usually has a shortdiscontinuity at the beginning and at the end of the event.However, while the event continues, the waveform again ex-hibits a cyclo-stationary behaviour. Therefore, it is difficultto discriminate it from normal operation using frequencybased or transform domain techniques. On the other hand,when the data is visualized in 2D, such an event produceshorizontal lines or edges. These lines may be difficult toobserve if the data is processed only in the horizontal di-rection. However, using the proposed method, we have theflexibility of processing the 2D data in the vertical direc-tion as well. A filter which has a high-pass characteristicin the vertical direction, therefore, clearly emphasizes theoccurances and locations of such events.

III. 2D Analysis of Transient Data

In order to detect power quality disturbances in the 2Drepresentation, we propose using 2D–DWT which providesthe necessary horizontal, vertical, and diagonal high passfiltering. 2D–DWT can be thought as the direct 2D ex-tension of the regular one dimensional discrete wavelettransform. It is known that the discrete wavelet trans-form (DWT) is the projection of a discrete signal ontotwo spaces: the approximation space (ϕ(t)), and a seriesof detail (wavelet) spaces (ψ(t)). The implementation ofthis projection operations is done by discrete-time subbanddecomposition of input signals using filtering followed bydown–sampling. The relation between the filters in thisstructure (the filter bank) and the wavelet spaces is as fol-

lows:ϕ(t) =

∑n h0[−n]

√2ϕ(2t − n)

ψ(t) =∑

n h1[−n]√

2ϕ(2t − n)(1)

Practically, h0[n] is a low-pass filter and h1[n] is a high-passfilter.

For a 2D image of size M ×N , the DWT, hence the sub-band decomposition, is first applied to the rows (horizontalprocess), producing two M×N/2 matrices (denote by l andh). Then, the same decomposition structure is applied toeach of the previously obtained matrices. The whole opera-tion corresponds to one-level decomposition, and we obtainfour images, each with sizes M/2 × N/2 (denote by ll, lh,hl, and hh). The second-level decomposition correspondsto further decomposition of the ll image to produce llll,lllh, llhl, and llhh. For decomposing further, one shouldsimply proceed with the decomposition of the low-pass ap-proximation image at every stage. One-level decompositionstructure is illustrated in Figure 3.

H ( z)0

H ( z)1

2

2

(along rows)

(along rows)

H ( z)0

H ( z)1

2

2

(along columns)

(along columns)

H ( z)0

H ( z)1

2

2

(along columns)

(along columns)

l l

l h

h l

h h

Fig. 3. One level filterank implementation of 2D-DWT.

In terms of wavelet notation, one level of decompositioncorresponds to projecting the input signal onto four signalsubspaces:• The scaling function:

ϕ(x, y) = ϕ(x)ϕ(y)

• The wavelet functions:

ψV (x, y) = ψ(x)ϕ(y)ψH(x, y) = ϕ(x)ψ(y)ψD(x, y) = ψ(x)ψ(y)

It is important to observe that ϕ(x, y) (or the ll subim-age) resembles the original image shape with one–fourththe original size, whereas ψV (x, y) (or the hl subimage)contains vertical, ψH(x, y) (or the lh subimage) containshorizontal, and ψD(x, y) (or the hh subimage) contains di-agonal edge–like shapes in the original image.

Due to the above observation, when one level 2D-DWTis applied to the PQ data in 2D, the 2D wavelet subspacescontain more features than the 1D transform of the origi-nal waveform. Usually, any waveform distortion producesstrong horizontal edges on the 2D image. At the output


l l

l h

h l

h h

0

2

1

1

2

(along columns)

G ( z)0

2

(along columns)

G ( z)1

2

(along rows)

G ( z)0

2

(along columns)

G ( z)0

2

(along columns)

G ( z)1

2

(along rows)

G ( z)1

Fig. 4. Pre-processing and one level filterank implementation ofinverse 2D-DWT.

of 2D–DWT, the lh subspace automatically contains ver-tically band–pass–filtered 2D signal samples. As a result,regardless of the type of event, the waveform variation isalways clear in the lh image. It is noteworthy that lh imagecontains the necessary discriminating features even if thewaveform distortion is smooth, which is usually the case forsags and swells. Therefore, we found the lh subspace to bethe most useful subspace in terms of detection. Moreover,other detail subspaces, i.e. hl and hh, also contain band–pass information which indicates sharp waveform distor-tions. The structure of disturbances in different subspacesprovide us with some discriminating criteria for event iden-tification. Events that cause smooth variations such as sagsor swells exhibit disturbances in forms of horizontal linesin the lh subimage. In the hl subspace, such events mayinduce short disturbances at the transitions correspondingto the beginning and/or the end of the event. If the transi-tions are smooth without any high frequency fluctuations,they may not induce any effect in the hl subspace. Onthe other hand, if the event is of an arcing fault type, itwould induce pronounced short bursts of disturbances inall subspaces. The difference between these behaviors mayconstitute a means of event identification.

In order to combine the above information contained inseparate subspaces into a single feature datum, we synthe-size the subspace signals (i.e. lh, hl, and hh images) byinverse 2D–DWT, while ignoring the ll subspace. Inverse2D–DWT is implemented by a synthesis filter–bank as il-lustrated in Figure 4, where the branches consist of verticaland horizontal up–samplers (instead of down–samplers ofan analysis filter–bank) followed by synthesis filters. Theresult of the inverse 2D–DWT is a 2D image at the originalscale.

Before inverting the 2D–DWT, the ll subspace is sup-pressed because it contains an image which is approxi-mately the same 2D representation of the waveform itself,so it does not contain feature–only signals. Since the filter–bank implementation of inverse 2D–DWT requires all foursubspace images, we get rid of the ll subspace by setingits coefficients to zero. Because of eliminating the ll com-ponent, the resulting reconstructed image does not exhibitthe original oscillatory wave–like pattern. Instead, it is a

more high–pass image having mostly fault and waveformdisturbance components.

A logical improvement before the inverse transform is toamplify the samples in lh sub–image. It can be noted thatmost of the informative disturbance shapes occur in thelh sub–image, therefore it constributes most to the finalreconstructed feature signal.

The final refinement before the inverse transform is toclean the signal samples in subband images. Much of thesignals with small magnitudes do not correspond to featuresthat represent events, therefore we eliminated the smallmagnitudes by applying a threshold to the sub–images andsetting the smaller values to zero. This is a well knowntechnique commonly used for de–noising. There is a largeamount of literature about the selection of threshold fordenoising [9],[10]. However, the threshold selection tech-niques are mostly optimized for human perception of pho-tographic images. Therefore, in order to achieve a usefuldenoised signal for our purpose, we have experimentallytested various PQ event waveforms and determined sepa-rate thresholds for each subband.

At the end of the inverse transform, only the necessaryfeatures of the subspaces are scaled and combined (as inFigure 4). Since the resultant signal contains joined sig-nals of the feature–wise important subspaces, we call theoutput the “joint feature 2-D wavelet subspace”. At thispoint, the image can be reconstructed back to 1D usingthe raster–scan order, and can be called the “joint featurewaveform”. This waveform is almost an event driven fea-ture only subspace, skipping the signal characteristics ofthe original waveform. The events can be simply detectedby comparing the feature waveform samples with zero. Anynonzero sample corresponds to an event at the time instantof the sample. This detection could also be done in the 2Ddenoised representation. However, the 1D signal also pro-vides the event localization. Its ability to localize and spotthe time instance of an event constitutes the advantage ofthe joint waveform over the direct use of 2D wavelet sub-spaces. It must be noted that the 1D joint feature wave-form neither corresponds to, nor can be obtained from 1Dwavelet decomposition. Many of the nonzero samples ofthe joint waveform, specifically the ones produced by lowfrequency variations, come from the 2D processing of thedata.

Experimentally, we have observed that the general be-haviour of the sub–images and the joint feature waveformdo not change with different choices of wavelets, such asvarious orders of Daubechies wavelets, Coiflets, Morlets,etc. For the rest of the paper, we present the results ob-tained by using the celebrated Daubechies–2 filter bank forthe decomposition.

The 2D wavelet decomposition requires twice the numberof computations compared to 1D wavelet decomposition ofthe same data using the same wavelet filter bank. In thisaspect, considering all the computations required for de-composition, denoising, detection, and inverse transforma-tion, the total computational complexity of the proposedmethod is linearly proportional to any 1D wavelet based


detection method. Although this method was proposedas an off–line analysis tool, we have tested our algorithmwith a TI TMS320067C11 floating point DSP processor kitwhich samples the waveform at 8 kHz and uses Daubechies–2 wavelet filter banks. The 2D representation width andheight were set to 640 × 640. We have observed that, theDSP kit was capable of processing the waveform and de-tecting event samples in real–time.

IV. Experimental results

We have found the proposed method to perform well forthe detection of a variety of events. Consider one level 2D–DWT decomposition of a real life voltage waveform givenin Figure 5. During acquiring this 40 seconds long line-to-line voltage waveform, two different power quality eventsare staged. The events are line-to-ground arcing fault andtwo consequtive sags due to 3-phase induction motor start-up. In the 1D-DWT, the arcing faults are observed to bedetectable across various decomposition scales. However,the voltage sags are not apparent (Figure 6). On the otherhand, both the voltage sags as long horizontal edges andthe arcing faults as horizontal perturbations of short edgeintervals are clearly visible in the lh-subimage of 2D-DWTdecomposition. In Figure 7, the 2D-DWT data of Figure 5is transformed to 1D using the joint form and presented.In order to display the locations of voltage sag events, thecaptured waveform shown in Figure 7(a) is displayed fora duration of approximately 20 seconds. Both in the 1Dand 2D decompositions, the same Daubechies–2 filters areused. Because of the high sampling rate, oscillations in thefigure are not visible. The joint feature waveform usingonly the lh, hl, and hh subspaces and its denoised versionare given in Figure 7(b) and (c) respectively. The denoisedversion includes the waveform disturbances due to events,whereas it does not have any noise components. This isan excellent improvement for easier thresholding for com-parison. Notice that the arcing fault (the left-most peak)and two consecutive voltage sags due to induction motorstarting events are clearly visible as nonzero waveform sam-ples. Once this feature waveform is available, using a zero/ nonzero comparison, PQ events are clearly detected andlocalized. The joint feature waveform contains all the dis-criminating information from lh, hl, and hh sub–images.The advantage of using vertical processing of the 2D databecomes clear in the detection of the voltage sags. In Fig-ure 5, the hl sub–image carries similar information to the1D wavelet processing of the signal. Notice that, althoughthe arcing fault can be visually discriminated in hl sub–image, the voltage sag events are not visible. This is alsoverified by the 1D decomposition in Figure 6. Therefore itis observed that some sags without high frequency contentmay not be detected using 1D wavelet based techniques.On the other hand, even for this case, arcing faults, as wellas sags are visible in lh sub–image, which can only be ob-tained using 2D wavelets. These properties of sub–imagesalso provides a means of event discrimination. If the eventresults in high magnitude samples in lh, hl, and hh sub–images, then it corresponds to a high frequency variation,

arcing fault

sag

LL LH

HL HH

Fig. 5. One level 2D-DWT decomposition of an event data.

4 5 6 7 8 9 10 11 12−1

0

1si

gn

al

4 5 6 7 8 9 10 11 12−0.5

0

0.5

d3

4 5 6 7 8 9 10 11 12−0.2

0

0.2

d2

4 5 6 7 8 9 10 11 12−0.1

0

0.1

d1

Arcing fault

Voltage sag

time (sec)

Fig. 6. Three levels of 1D wavelet decomposition of data in Figure5.

resulting from arcing faults. On the other hand, if it isnot visible in hl and hh sub–images, but pronounced inlh sub–image, it corresponds to a waveform variation withlower frequency content, such as a voltage sag or a sub–fundamental interharmonic contamination.

We have also observed that a specific power quality dis-turbance, the frequency fluctuations, can be detected byexamining the ll subspace. In Figure 5, the wave segmentsare not straight and this implies a frequency fluctuation.Furthermore, the tilt in the sinusoidal alignment indicatesthat the fundamental frequency is slightly less than theexpected 50Hz.

In the next example, the effects of interharmonic volt-ages and currents are examined. Interharmonics are im-portant PQ events that may be due to adjustable speeddrives. They appear as steady state currents or voltages at


5 10 15 20 25−1

−0.5

0

0.5

2 4 6 8 10 12 14 16 18 20 22−0.3

−0.2

−0.1

0

0.1

2 4 6 8 10 12 14 16 18 20 22

−0.2

−0.1

0

0.1

0.2

time(sec)

voltage

(a)

(b)

(c)

arcing fault voltage sag

Fig. 7. Joint feature waveform of data in Figure 5.

29.95 30 30.05 30.1 30.15 30.2 30.25 30.3 30.35 30.4−1.5

−1

−0.5

0

0.5

1

time (sec)

voltage

effect of interharmonics

Fig. 8. Voltage waveform with interharmonics.

non–integer multiples of the fundamental frequency. Thewide–band interharmonics are usually noise–like and eas-ier to detect, whereas sub–fundamental interharmonics aremuch more difficult to detect. In order to test the pro-posed method for both cases, we added a wide–band in-terharmonic and two narrow–band interarmonics at 25 Hzand 185 Hz with 1% of the voltage magnitude. Notice thatneither 25 Hz nor 185 Hz are integer multiples of 50 Hz.Specifically, the 25 Hz. interharmonic is almost impossibleto detect even by the expert eye (Figure 8).

The 2D–DWT of the data corresponding to Figure 8 isdepicted in Figure 9. Notice that wide–band and sub–fundamental interharmonics are clearly visible, especiallyin the lh sub–image. On the other hand, the hl sub–image, which carries similar information to the 1D waveletdecomposition, is unable to depict the sub–fundamentalinterharmonic. When the ll image is omitted and inverse2D–DWT is applied, we obtain the 1D feature waveformin Figure 10(b). By further de–noising, the joint featurewaveform is obtained as in Figure 10(c). The nonzero mag-nitude samples correspond to events at the nonzero sampleinstances.

As a last example, we take another real life event of

LL LH

HL HH

wide−band disturbance

interharmonics

Fig. 9. One level 2D–DWT decomposition of voltage waveform withinterharmonics.

29.8 30 30.2 30.4 30.6 30.8 31 31.2 31.4

−1

−0.5

0

0.5

1

time (sec)

5 10 15 20 25 30

−0.1

0

0.1

5 10 15 20 25 30

−0.1

0

0.1

interharmonics

wide−band disturbance

(a)

(b)

(c)

time (sec)

time (sec)

Fig. 10. Feature waveform of data in Figure 9.

phase–to–ground arcing fault. During this experiment arc-ing fault recovers after several cycles of initiation and thenstrikes back again for several more cycles. From Figure 11,it is again apparent that the events are clearly visible inthe approximation sub–images: lh, hl, and hh. In order toobtain a single feature waveform, and to localize the events,the described joint data is obtained from the approxima-tion sub–images, and denoised in Figure 12.

V. Conclusions

In this paper, 2D representation and analysis of PQ eventdata is introduced. The 2D representation is observed tohave advantages over the classical 1D data representationin terms of PQ event analysis and detection. In order toachieve event analysis, we used 2D-DWT decomposition of


Arcing Fault

Fig. 11. One level 2D–DWT decomposition of voltage waveform witharcing fault.

0.7 0.8 0.9 1 1.1 1.2

−0.4

−0.2

0

0.2

0.4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−0.5

0

0.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−0.5

0

0.5

time (sec)

Arcing fault time (sec)

time (sec)

Fig. 12. Feature waveform of data in Figure 11.

the 2D representation. Due to the vertical and horizontalprocessing capability of the 2D-DWT, PQ events even withslow waveform variations were possible to detect.

References

[1] O. N. Gerek and D. G. Ece, ”2-D Analysis and Compression ofPower Quality Event Data,” IEEE Trans. on Power Delivery,Vol. 19, No. 2, April 2004.

[2] Wael R. Anis Ibrahim and Medhat M. Morcos, “Artificial In-telligence and Advanced Mathematical Tools for Power QualityApplications: A Survey”, IEEE Trans. on Power Delivery, Vol.17, No. 2, April 2002.

[3] L. Angrisani, P. Daponte, and M. D’Apuzo, “Wavelet Network-Based Detection and Classification of Transients”, IEEE Trans.on Instrument. and Meas., Vol. 50, No. 5, 2001

[4] Surya Santaso, W. Mack Grady, and Edward J. Powers, “Char-acterization of Distribution Power Quality Events with Fourier

and Wavelet Transforms”, IEEE Trans. on Power Delivery, Vol.15, No. 1, 2000.

[5] A. M. Gaouda, M .M. A. Salama, M. R. Sultan, and A. Y.Chikhani, “Power Quality Detection and Classification UsingWavelet-Multiresolution Signal Decomposition”, IEEE Trans.on Power Delivery, Vol. 14, No.4, 1999.

[6] S. J. Huang and C. T. Hsieh, “High Impedance Fault DetectionUtilizing a Morlet Wavelet Transform Approach”, IEEE Trans.On Power Delivery, Vol. 14, No. 4, 1999.

[7] T. Zheng, E. B. Makram, and A. A. Girgis, “Power System Tran-sient and Harmonic Studies Using Wavelet Transform”, IEEETrans. on Power Delivery, Vol. 14, No. 4, 1999.

[8] T. B. Littler and D. J. Morrow, “Wavelets for the Analysis andCompression of Power System Disturbances”, IEEE Trans. onPower Delivery, Vol. 14, No. 2, April 1999.

[9] S. Sardy, “Minimax threshold for denoising complex signals withWaveshrink,” IEEE Trans. on Signal Processing, Vol. 48, No. 4,2000.

[10] G. Shi, F. Li, “Image Denoising with Optimized SubbandThreshold,” Proc. 5th Int.’l Conf. on Computational Intelli-gence and Multimedia App. (ICCIMA’03), Sep. 27 - 30, 2003.

Dogan Gokhan Ece was born in Ankara,Turkey in 1964. He received the Engineerdegree from Istanbul Technical University in1986, the M.Sc. and Ph.D. degrees from Van-derbilt University, Nashville, Tenn., in 1990and 1993, respectively all in electrical engineer-ing. Currently he is professor of Electrical andElectronics Engineering in Anadolu University.His research areas include power quality, faultdetection, and modelling.

Omer Nezih Gerek was born in Eskisehir,Turkey in 1969. He received the Engineer,M.Sc., and Ph.D. degrees from the Bilkent Uni-versity in 1991, 1993, and 1998, respectively, allin electrical engineering. Following his Ph.D.,he spent one year as a research associate atEPFL, Switzerland. Currently he is professorof Electrical Engineering in Anadolu Univer-sity. His research areas include signal analysis,wavelets, and subband decomposition.

pq event detection using joint 2d-wavelet subspaces

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