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Synopsis of the thesis

Entitled

APPLICATIONS OF WAVELETS TO POWER SYSTEMS To be Submitted

To

VISHVESHVARAYA TECHNOLOGICAL UNIVERSITY , BELGAUM

Research Center

DEPARTMENT OF ELECTRICAL ENGINEERING

SDM COLLEGE OF ENGINEERING AND TECHNOLOGY

DHARWAD KARNATAKA STATE (INDIA)

For the Degree of

Doctor of Philosophy

In

ELECTRICAL ENGINEERING

By

V. R. Sheelavant

Research Guide

Dr. Vijaya C.

M.Tech., Ph.D

Professor

DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING

SDM COLLEGE OF ENGINEERING AND TECHNOLOGY

DHARWAD KARNATAKA STATE (INDIA)

Co- Guide

Dr. S.C. Shiralashetti

Msc., M.Phil.PGDCA., Ph.D

Asst. Professor

DEPARTMENT OF MATHEMATICS

SDM COLLEGE OF ENGINEERING AND TECHNOLOGY

DHARWAD KARNATAKA STATE (INDIA)

JANUARY-2009

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APPLICATIONS OF WAVELETS TO POWER SYSTEMS

Wavelet based algorithms have found many uses in different areas. Most of them are to signal processing

or numerical analysis. Here is a plan to study some of applications in power system. The synopsis for

Ph.D proposed work is organized as follows.

The first part is devoted to the historical background of wavelets. Second part is concerned with

the fault detection in power system by wavelets. Part three is mainly concerned with disturbance and

variation detection in power system by using wavelets. Fourth part devoted to the denoising of electrical

signals by using wavelets. Last part is concerned with data compression.

INTRODUCTION: It is indeed twenty years ago, in 1982, that a French engineer working on

seismological data for an oil company, Jean Morlet , proposed the concept of wavelet analysis to reach

automatically the best trade-off between time and frequency resolution[1,2]. Later this proposition has

been considered as an extension of the ideas of Haar (1910) and Gabor (1946) [3] , themselves being

Fourier’s followers(1888). As any discovery in science, wavelets resulted from numerous contributions,

they are based on concepts that already existed before Morlet’s idea and, clearly, it was in the mood of the

signal processing community in the 1980’s. Quickly after this seminal proposition the main elements have

been fixed by Y. Meyer (1985) [4] , S. Mallat (1987)[5] ,I. Daubechies (1988)[6] , and then numerous

other contributors brought their stone in the 1990’s amongst them a special mention to the lifting scheme

and second generation wavelets proposed by W. Sweldens (1995) [7] should be done.

Even more recently (2003) some very exciting papers have been published about new ideas

(ridgelets[8, 9] , curvelets[10] , fresnelets etc.), which show that the subject is still alive and a rich

ground for innovative propositions to blossom. The wavelet transform, multiresolution analysis, and other

space frequency or space scale approaches are now considered standard tools by researchers in signal

processing, and many applications have been proposed that point out the interest of these techniques. The

most known application field of wavelet transform is image compression for still and video imaging. This

tool is included in the new norms JPEG and MPEG where it replaced the classical Discrete Cosine

Transform. In audio and, more precisely, automatic speech analysis, the wavelets are currently in the

operational softwares. However, even though promising practical results in power systems ,machine

vision for industrial applications have recently been obtained, wavelet transform in operational industrial

products is still rarely used and a lot of ideas are still to be involved in industrial imaging projects. The

reason may be , sometimes abstruse, mathematics involved in wavelet text books or on the contrary the

false faith in the omnipotence of this new tool leading to disappointing experiences. Be that as it may, it

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seems more than ever necessary to propose opportunities for exchanging between practitioners and

researchers about wavelets. As a part of this proposed work , the recently published works dealing with

power systems applications of wavelet and, more generally speaking, multiresolution analysis will

reviewed.

FAULT DETECTION IN POWER SYSTEMS: Basic power system protection principles are outlined in

standard literature [11, 12]. The primary purpose of power system protection is to ensure safe operation of

power systems, thus to care for the safety of people, personnel and equipment. Furthermore, the task is to

minimize the impact of un-avoidable faults in the system. From an electrical point of view, dangerous

situations can occur from over currents and overvoltage. According to [13], [14], and [15], the voltages

occurring on system’s insulators have diversified origins of formations. In the normal operating process,

the values of normal operation AC voltages (or normal operation DC voltages in the DC transmission

networks like HVDC) do not affect the insulation breakdown of elements in the system. However, these

values will decide the initial conditions of overvoltage waves arising from the operation.

Generally, the over-voltages occurring within the power systems can be classified into 2 main

types: External over-voltages: Forming by the atmospheric disturbances in which lightning stroke is the

primary cause. Internal over-voltages: caused by changes of the power systems’ operating condition. The

internal over-voltages can be divided into: Switching over-voltages Temporary over-voltages . As

already known, overvoltages occurring in power systems are primarily internal overvoltages, arising

abundantly under system operating levels. The switching of transmission lines, loads, high-voltage

capacitors or transformers can cause internal over-voltages. These over-voltages appear with a high

frequency but with a negligible influence on the normal working condition of the network’s insulators.

Moreover, amplitudes of the oscillations are not very large and the density of inside disturbances are not

very high in comparison to ones of external over-voltages’. In the deregulated generation environment the

overvoltages and change in current in magnitude as well as direction are invited to occur. External over-

voltages are caused mainly by natural impacts such as direct and indirect lightning. The lightning may

strike the lines directly, creating external over-voltages transmitting in opposite directions. Otherwise,

lightning may indirectly strike the protecting lines, bringing faradic over-voltages on the lines’ phases.

The Fourier transform has been a very powerful tool which was widely used in signals analyzing and

processing. However, this traditional method is not appropriate to analyze non-stationary signals. To

overcome this difficulty, the traditional Fourier transform has been improved into the Short Time Fourier

Transform (STFT) by applying the Fourier transform onto every each small part of the signals. Yet the

STFT still has a drawback regarding the inflexibility of the time frequency resolution, and it is still

unsuitable for non-stationary signals like the over-voltages signals in reality. Those shortcomings have

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lead to the foundation of Wavelet transform recently. Hence , in the second part, the different methods of

detecting various faults in the deregulated power system using wavelets will be explored.

DISTURBANCE DETECTION IN POWER SYSTEMS: Electric power quality is an important issue in

power systems nowadays .The demand for clean power has been increasing in the past several years. The

reason is mainly due to the increased use of microelectronic processors in various types of equipments

such as computer terminals, programmable logic controllers and diagnostic systems. Most of these

systems are quite susceptible to disturbances in the supply voltage. For example a momentary power

interruption or thirty percent voltage sag lasting for hundredth of a second can reset the PLCs in an

assembly line. The amount of waveform distortion has been found to be more significant nowadays due to

the wide applications of nonlinear electronic devices in power apparatus and systems. Without

determining the existing levels of power quality, electric utilities cannot adopt suitable strategies to

provide a better service in the deregulated generation system. Therefore an efficient approach of

justifying these electric power quality disturbances is motivated. Several research studies regarding the

power quality have been conducted. Their aims were often concentrated on the collection of raw data for

a further analysis, so that the impacts of various disturbances can be investigated. Sources of such

disturbances can be located or further mitigated. However, the amount of acquisition data was often

massive in their test cases. Such an abundance of data may be time consuming for the inspection of

possible culprits. A more efficient approach is thus required in the power quality assessment. The

implementation of the discrete Fourier transform by various algorithms has been constructed as the basis

of modern spectral analysis. Such transforms were successfully applied to station signals where the

properties of signals did not evolve in time. However, for those non-stationary signals any abrupt change

may spread over the whole frequency axis. In this situation, the Fourier transform is less efficient in

tracking the signal dynamics[16]. A point -to- point comparison scheme has been proposed to discover

the dissimilarities between consecutive cycles[17]. This approach was feasible in detecting certain kinds

of disturbances but fail to detect those disturbances that appear periodically.

With the introduction of new network topologies and improved training algorithms, neural

network technologies have demonstrated their effectiveness in several power system applications [18].

Once the networks have been well trained, the disturbances that correspond to the new scenario can be

identified in a very short time[19]. This technique has also been applied in the power system applications.

However, it can only be applied to detect a particular type of disturbance. When encountering different

disturbances, the network structure has to be reorganized, plus the training process must be restarted. A

method of detecting power quality disturbances based on Artificial Neural Networks (ANN) and wavelets

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has been proposed[20]. In this method, the fundamental component is removed using wavelets and the

remaining signal corresponding to disturbances is processed and given as input to ANN. However, this

method fails to detect voltage sag/swell and also new ANN’s have to be developed for different rated load

voltages and sampling frequencies. Recently with the emergence of wavelets it has paved a unified

framework for signal processing and its applications[21]. Fourier transforms rely on a uniform window

for spread frequencies. Wavelet transforms can apply various lengths of windows according to the

amount of signal frequencies. Characteristics of non- stationary disturbances were found to be more

closely monitored by wavelets. The transient behavior, cavities and discontinuities of signals can be all

investigated by wavelet transforms. For example, if there is an instantaneous impulse disturbance, which

happens at a certain time interval it may contribute to the Fourier transform, but its location on the time

axis is lost. However, by wavelets both time and frequency information can be obtained. In other words,

the wavelet transform are more local. Instead of transforming a pure ‘time domain’ in to a pure’

frequency domain ’, the wavelet transforms find a good compromise in time - frequency domain. Hence

the third part of the proposed work presents novel algorithm, which overcomes all these difficulties and

can accurately detect and classify the disturbances present in the power system signal. We will find a

method, which is independent of the load voltage and can be easily customized for different sampling

frequencies. In this approach, for detecting each disturbance a particular wavelet would be used. The

method uses wavelet filter banks in an effective way and does multiple filtering to detect the disturbances.

The performance evaluation of different wavelets in the proposed method shows the capability of a

particular wavelet in detecting a particular disturbance.

DENOISING OF ELECTRICAL SIGNALS: In electric drives applications the use of signal

transformations is very common. Among others, the Laplace and the z-transforms are used for designing

controllers while the Fourier transform is primarily used for designing filters that will remove unwanted

noise components from useful measurements. A relatively new technique in this is the wavelet transform

with most applications in fault detection and condition monitoring [22-24]. It is found that the use of

wavelets provides additional tools to monitor electric drives applications, with considerable advantages

comparing to convectional detection techniques, which for example measure the �i/ �t of the phase

currents. It is well known, in the digital signal processing community, that wavelets revolutionized data

compression applications by offering compression rates which other methods could not achieve [25].

Another application similar to compression is wavelet shrinkage, which allows the de-noising of useful

signals without focusing on specific frequency coefficients [26]. As was reported in [26] simple drives

denoising schemes (based on FIR filters) produced similar results to those of wavelets. Hence wavelets

should not be applied for these applications since they are more complex than simple FIR filters.

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Wavelets can prove [26] to be more successful in sensorless speed control applications, [27]. In these

cases the useful information (rotor speed) is modulated by an injected high frequency signal and

demodulating methods that are based on wavelets produce better results. Another equally popular method

to estimate the rotor speed is to use a Kalman filter [28] which has good estimation characteristics but its

correct use is heavily correlated with good estimate of the noise properties of the current sensors .Fourth

part of the proposed work addresses these two very important issues in the control of electrical machines,

correct denoising and proper estimation of the noise components in the current measurements. A solution

based on wavelets will be proposed which greatly improves the behavior of the estimation technique.

DATA COMPRESSION IN PQ MONITORING: Increasing interest in power quality (PQ) has evolved

over the past decade [29]. With the advancement of PQ monitoring equipment, the amount of data

gathered by such monitoring systems has become huge in size. The large amount of data imposes

practical problems in storage and communication from local monitors to the central processing

computers. Data compression has hence become an essential and important issue in PQ area. A

compression technique involves a transform to extract the feature contained in the data and a logic for

removal of redundancy present in extracted features. For PQ issues the discrete cosine transform (DCT) is

conventionally used for data compression because of its orthogonal property [30].

In recent past, the DWT has emerged as a potential tool for data analysis [31,32], de-noising and

compression [33,34] of different signals as it provides relatively efficient representation of piecewise

smooth signals [35]. The degree to which a wavelet basis can yield sparse representation of different

signals depends on the time-localization and smoothness property of the basis function. Data compression

can be also accomplished by neural network approach as proposed in [36].Among the varieties of wavelet

functions the spline wavelet (SW) is the best one on the basis of time-localization and smoothness

properties [37–39]. In a recent paper [40] the SW transform (SWT) is proposed for PQ data compression

but, for a requirement of high compression of signals the wavelet transform approach may not provide a

satisfactory result. Investigation will be made to overcome this problem by using suitable wavelets.

Conclusion :As wavelet based algorithms are applicable to local and global analysis of signals , lot

of work has been done as their applicability in concerned with power system. The work being done

is visualization of electrical transients, Fault detection in shipboard power systems which are single

phase type, protection of alternator , noise reduction in electrical signals , Power quality

disturbance data compression using wavelet transform methods. With reference to this work ,

wavelet based algorithms may be developed for , fault detection, disturbance detection , noise

reduction in electrical drives ,data compression in a deregulated power system environment .

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REFERENCES

1. A. Grossman, J. Morlet, ”Decomposition of Hardy functions into square integrable wavelets of

constant shape”, SIAM J. Math. Anal., 15, pp. 723-736, 1984.

2. J. Morlet, G. Arens, E. Fourgeau, D. Giard, ”Wave propagation and sampling Theory 1,

complex signal and scattering in multilayered media”, Geophysics, 47, pp. 203-221, 1982.

3. D. Gabor, Journal of Inst. Electr. Engin., 93, pp. 429, 1946.

4. Y. Meyer, Ondelettes et opérateurs I: Ondelettes, Herman, Paris, 1990.

5. S.Mallat, ”A theory for multiresolution signal decomposition; the wavelet

representation”, IEEE trans. on PAMI, 11(7), pp. 674-693, july 1989.

6. D. Cornforth, R.Middleton, J. Tusek, ”Visualisation of electrical transient using

the wavelet transform”, proc. of AISTA 2000, 2000.

7. W. Sweldens, The lifting scheme: a construction of second generation wavelets,

Tech. report 1995:6, Industrial Math-ematics Initiative, Dpt of Math., University

of South Carolina, 1995.

8. E.J. Candès, Ridgelets: theory and applications, Ph.D. dissertation, Dept.

Statistics, Stanford University, 1998.

9. M.N. Do, M. Vetterli, ”The finite ridgelet transform for image representation”,

IEEE . Trans. on Image Processing, 12(1),pp. 16-28, jan. 2003.

10. D.L. Donoho, M.R. Duncan, ”Digital curvelet transform for image denoising”,

proc. of SPIE, vol. 4056, pp. 12-29,2000.

11. A.R. Bergen and V. Vittal. Power systems analysis. Prentice Hall, 2nd edition,

2000. ISBN 0-13-691990-1.

12. L. MÄuller and E. Boog. Selektivschutz elektrischer Anlagen. VWEW Verlags-

Und Wirtschaftsgesellschaft der ElektrizitÄatswerke, 2nd edition, 1990. ISBN

3- 8022-0218-X [in German].

13. N. Jenkins et al. Embedded generation. IEE, 2000. ISBN 0-85296-774-8.

14. G. Koeppel. Distributed generation. Literature and current state review, Swiss

Federal Institute of Technology Zurich, EEH - Power Systems Laboratory, 2003.

15. N. Jenkins. Embedded generation. Power Engineering Journal,9(3):145{150,

1995.

16. Malay, S. and W.L. Hwang, 1992. Singularity detection and processing with

wavelets. IEEE Trans. Information Theory, 38: 617-643.

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17. Ghosh, A. and G. Ledwich, 2002. Power Quality Enhancement Using Custom

Power Devices. Kluwer Academic Publishers, USA.

18. Santoso, S., E.J. Powers, W.M. Grady and A.C. Parsons, 2000. Power quality

disturbance waveform recognition using wavelet-based neural classifier. I.

Theoretical foundation. IEEE Trans. Power delivery, 15: 222-228.

19. Wilkinson, W.A. and M.D. Cox, 1996. Discrete wavelet analysis of power system

transients. IEEE.Trans. Power Systems, 11: 2033-2044.

20. Perunicic, B., M. Mallini, Z. Wang and Y. Liu, 1998. Power quality disturbance

detection and classification using wavelets and artificial neural networks. Proc.

Harmonics and Quality of Power,1: 77-82.

21. Heydt,G.T. and A.W. Galli, 1997. Transient power quality problems analyzed using

wavelets. IEEE Trans. Power Delivery, 12: 908-915.

22. F. Briz, M.W. Degner, A. Diez and R.D. Lorenz, “Sensoless position control of

permanent magnet synchronous machines without limitation at zero speed”, IEEE

Trans Ind Apps, vol. 38, no. 3, May/June 2003, pp. 670- 678.

23. L. Eren and M.J. Devaney, “Bearing damage detection via wavelet packet

decomposition of the stator current”, IEEE Trans Instr and Meas, vol. 53, no. 2, April

2004, pp. 431 – 436.

24. L. Jianguo Liu, P. Pillay P and H. Douglas, “Wavelet modeling of motor drives

applied to the calculation of motor terminal overvoltages”, IEEE Trans Ind-

Electronics, vol. 51, no. 1, Feb. 2004, pp. 61 – 66.

25. L.D. Donoho, “De-noising by soft-thresholding”, IEEE Trans Inf Th, vol. 41, no. 3,

May 1995, pp. 613 – 627.

26. D. Giaouris and J.W. Finch: “Denoising using wavelets on electric drives

applications”, Electric Power Systems Research, submitted.

27. M. Linke, R. Kennel and J. Holtz: “Static and dynamic behavior of saturation-induced

saliencies and their effect on carrier-signal-based Sensorless AC drives”, IECON

2002, vol. 1, 5-6 Nov 2002, pp. 674 – 679.

28. D.J. Atkinson, P.P. Acarnley and J.W. Finch, “Observers for induction motor state

and parameter estimation”, IEEE Trans Ind Apps, vol. 27, no. 6, Nov/Dec 1991, pp.

1119 – 1127.

29. J. Arrillaga, M.H.J. Bollen, N.R. Watson, Power quality following deregulation, IEEE

Proc. 88 (2) (2000) 246–261.

31. K.R. Rao, P. Yip, Discrete Cosine Transform: Algorithms, Advantages, and

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applications, Academic Press, New York, 1990.

32 .S. Santoso, et al., Power quality assessment via wavelet transform analysis, IEEE

Trans. Power Delivery 11 (1995) 924–930.

33. L. Angrisani, et al., A measurement method based on the wavelet transform for power

quality analysis, IEEE Trans. Power Delivery,No. PE-056-PWRD-0-1-1998.

34. S. Santoso, E.J. Power, W.M. Grady, Power quality disturbance data compression

using wavelet transform methods, IEEE Trans. Power Delivery 12 (3) (1997) 1250–

1256.

35. T.B. Littler, D.J. Morrow, Wavelets for analysis and compression of power system

disturbances, IEEE Trans. Power Delivery 14 (2) (1999) 358–364.

36. G. Strange, T. Nguyen, Wavelets and Filterbanks, Wellesley- Cambridge, Wellesley,

MA, 1996.

37. A. Namphol, S.H. Chin, M. Arozullah, Image compression with a hierarchical neural

network, IEEE Trans. Aerospace Electron. Syst. 32 (1) (1996) 326–338.

38. M. Unser, Splines: A perfect fit for signal and image processing, IEEE Signal

Process. Mag., November 1999.

39. A. Cohen, I. Daubechies, J.C. Feauveau, Bi-orthogonal bases of compactly supported

wavelets, Comm. Pure Appl. Math. 45 (1992)485–560.

40. C.K. Chui, J.Z. Wang, On compactly supported spline wavelets and a duality

principle, Trans. Am. Math. Soc. 330 (2) (1992) 903–915.

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