Olkkonen J. (ed.) Discrete Wavelet Transforms - Theory and Applications
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Benign Malignant
Benign 28 (80%) 7 (20%)
Malignant 8 (42%) 11 (58%)
Table 6. Results f or mammogram ROI classification.
9. Conclusions
A total of 75 abnormal and normal bowel images were co rrectly classi fied at an average rate of
85%, 86 retinal images had an average classification accuracy of 82.2% and the mammog ram
lesions (54) were classified correctly 69% on ave rage. The classification results are quite high,
considering that the system wasn’t tuned for a specific modality. The system performed well,
even though: (1) pathologies came in various orientations, (2) pathologies arose in a variety
of locations in the image, (3) the masses and lesions were of various sizes and shapes and
(4) there was no restriction on the type of pathology for the retinal and small bowel images.
Accounting for all these scenarios in one algorithm was a major challenge while designing
such a unified framework for computer-aided diagnosis.
Although the classification results are high, any misclassification can be accounted to cases
where there is a lack of statistical differentiatio n between the texture uniformity of the
pathologies. Additionally, normal tissue can sometimes assume the properties of abnormal
regions; for example, consider a normal small bowel image which has more than the average
amount of folds. This may be characterized as non-unifor m texture and consequently would
be misclas sified. In a normal retinal image, if the patie nt has more than the average number
of vessels in their eye, this may be detected as oriented or heterogeneous texture and could
be misclassified. Moreover, when considering the mammogram lesions, the normal breast
parenchyma is overlapping with the lesions and also assumes some textural properties itself.
In order to improve the performance of the mammogram lesions, a segmentation step could
be app lied prior to feature extraction.
Another important consideration arise s from the database sizes. As was stated in Sectio n 7, the
number of images used for classificati on can determine the accuracy of the estimated classi fier
parameters. Since only a modest number of images were used, misclassification could result
due to the lack of proper estimation of the classifiers parameters (although the scheme tried
to combat this with LOOM). This could be the case for the mammogram lesions especially,
since the number of benign lesions outnumbered the malignant lesions by almost double -
this could have caused difficulties in classificati on parameter accuracy. Additionally, finding
the right trade off between number of f eatures and database size is an ongoing research topic
and has yet to be perfectly defined Fukunaga & Hayes (1989).
The overall success of the system is a result of the design of the algorithm, which aimed
to account for all the pathological scenarios previously described. Firstly, the utilization of
the DWT was important to gain a space-localized represe ntation of the im ages’ elementary
texture units (tex tons), whi ch is in accordance to human texture perce ption. Secondly,
the choice of wavelet-based statistical texture measures (entropy and homogeneity) was
critical in quantifying the localized texture properties of the images (which provided
discrimination between normal and other pathological cases). Utilization of the SIDWT
allowed for the extraction of consistent (i.e. shift-invariant) features. Fu rthermore, due to
the scale-invariant basis functions of the DWT, pathologies of varying sizes were captured
within one transformation (i.e. the features were scale-invariant).
By design, the system is relatively robust to pathologies which occurred in various
orientations. Features were collected at various angles (0
◦
, 45
◦
, 90
◦
, 135
◦
) in the respective
subbands in order to describe the texture eleme nts, regardless of their orientation. The fe ature
set thus offered a semi-rotational invariant rep resentati on which could account for oriented
textural properties (of pathology).
A last point for discussion is the fact that features were successfully extracted from the
compressed domain in the retinal and small bowel images. Since many forms of multi-media
are being stored in lossy formats, it is important that cl assificati on systems may al so be
successful when utilized in the compressed domain.
A generalized framework for computer-aided diagnosis was designed in accordance to the
human texture perception model. The uni fied feature extraction and classification scheme
utilized the DWT and textural features were extracted from the wavelet domain for a localized
description of the relative homogeneity of the images. To ensure the DWT representation was
suitable for the co nsiste nt extraction of features, a shift-invariant discrete wavelet transform
(SIDWT ) was computed. To combat the small database si ze, a small number of features
and LDA classificatio n were used in conjunction with the LOOM to gain a more accurate
approximation of the classifier’s parameters.
A total of 75 abnormal and normal bowel images were co rrectly classi fied at an average rate of
85%, 86 retinal images had an average classification accur acy of 82.2% and the mammog ram
lesions (54) were classi fied correctly 69% on average. The success of the system can be
accounted to the semi-rotational invariant, scale-invariant and shift-i nvariant features, which
permitted the extraction of discriminating features regardless of the location, shape, size or
orientation of the pathologies.
10. References
Adams, M. D . & Ward, R. K. (2003). Symmetric-exte nsion-compatible reversible
integer-to-integer wavelet transforms, IEEE Transactions on Signal Processing
51(10): 2624–2636.
Armstrong, A. & Jiang, J. (2001). An efficient image indexing algorithm in JPEG compressed
domain, International Conference on Image Process ing, pp. 350–351.
Beylkin, G. (1992). On the representation of o perato rs in bases of compactly supported
wavelets, SIAM Journal of Numerical Analysis 29: 1716–1740.
Bradley, A. ( 2003). Shift-invariance in the discrete wavelet transform, Digital Imag e
Computing: Techniques and Applications, pp. 29 – 38.
Brandon, L. & Hoover, A. (2003). Drusen detection in a retinal image using multi-level
analysis, Vol. 1, MICCAI, pp. 618–625.
Burrus, C., Gopinath, R. & Guo, H. (1998). Introduction to Wavelets and Wavelet Transforms - A
Primer, Prentice Hall International, Inc., Houston, Texas.
Chang, S. (1995). Compres sed- domain techniques for image/video indexing and
manipulation, Vol. 1, International Conference on Image Processing , pp. 314 – 317.
Cheng, H. D., S hi, X. J., Min, R., Hu, L. M., Cai , X. P. & Du, H. N. (2006). Appro aches
for automated detection and classification of masses in mammograms, Pattern
Recognition 39(4): 646–668.
Chiu, C., Wong, H. & Ip, H. H. S. (2004). Compressed domain feature transformation using
evolutionary strategies for image classification, Vol. 1, International Conference on
Image Processing, pp. 429 – 432.
209
Shift-Invariant DWT for Medical Image Classification
Cohen, I., Raz, S. & Malah, D. (1997). Orthonormal shift i nvariant wavelet packet
decomposition and representation, Elsevier: Signal Processing 57: 251–270.
Coif man, R. R. & Saito, N. (1995). Local dis criminant bases and their applicati ons, Journal of
Mathematical Imaging and Vision 5: 337–358.
Coif man, R. R. & Wickerhauser, M. V. (1992). Entropy-based algorithms for best basis
selection, IEEE Transacti ons on Information Theory 38: 713 – 718.
Denecker, K., Assche, S. V., Phillips, W. & Lemahieu, I. (1997). State of the art concerning
lossless medical image coding, PRORISC IEEE Benelux Workshop on Circuits,
Syste ms and Signal Process ing, pp. 129–136.
Fernández, G., Periaswamy, S. & Sweldens, W. (1996). LIFTPACK: A software package for
wavelet transforms using lifting, Proceedings of the SPIE - Wavelet Applications in
Signal and Image Proc essing IV, pp. 396–408.
Ferreira, C. B. R. & Borges, D. L. (2001). Automated mammogr am classification using
a multiresolution pattern recognition approach, Proceedings of XIV Brazilian
Symposium on Computer Grap hics and Image Processing, pp. 76 – 83.
Fukunaga, K. & Hayes, R. R. (1989). Effects of sample size in classifier de sign, IEEE Transactions
on Pattern Analysis and Machine Intelligence 11(8): 873 – 885.
Given Imaging Ltd. (2006a). Patient Brochure, World Wid e Web.
http://www.givenimaging.com/Cultures /en-US /Given /English/Professionals/.
Given Imaging Ltd. (2006b). Patient Information Guide, World Wide Web.
http://www.givenimaging.com/Cultures/en-US/Given/English/Patients/.
Given Imaging Ltd. (2006c). PillCam
TM
SB Capsule Endoscopy - Product Information Guide, World
Wide Web. http://www.givenimaging.com/Cultures /en-US /Given/English
/Products/CapsuleEndoscopy/.
Goldbaum, M. (2002). STARE - STructured Analysis of the Retina, World Wide Web.
http://www.parl.clemson.edu/stare/.
Guliato, D., Rangayyan, R. M., de Carvalho, J. D. & Santiago, S. A. (2007). Polygonal
modeling of contours of breast tumors with the preservation of spicules, IEEE Trans.
on Biomedical Engineering .
Haijiang, T., Sei-Ichiro, K., Kazuyuki, T. & Masa- Aki, K. (2004). Lossless image com pression
via multi-scanning and adaptive linear prediction, Vol. 1, The 2004 IEEE Asia-Pacific
Conference on Circuits and System s, pp. 81–84.
Julesz, B. (1981). Textons, the elements of texture perception, and their interactions, Nature
290(5802): 91–97.
Khademi, A. (2006). Multiresolutional analysis for classi�cation and compression of medical images,
Master’s thesis. Ryerson Univers ity, Canada.
Khademi, A. & Krishnan, S. (2006). Multiresolution analysis and classification of small bowel
medical images, Proceedings of IEEE Engineering in Medicine and Biology, pp. 4524
– 4527.
Khademi, A. & Kr ishnan, S. (2007). Shift-invariant discrete wavelet transform anal ysis for
retinal image classification, Journal of Medical and Biological Engineering and Computing
pp. 1–12. in press - online first.
Khademi, A. & Krishnan, S. (2008). Medi cal image texture analysis: A case study with small
bowel, retinal and mammogram images, IEEE CCECE, pp. 1–6.
210
Discrete Wavelet Transforms - Theory and Applications
Cohen, I., Raz, S. & Malah, D. (1997). Orthonormal shift i nvariant wavelet packet
decomposition and representation, Elsevier: Signal Processing 57: 251–270.
Coif man, R. R. & Saito, N. (1995). Local dis criminant bases and their applicati ons, Journal of
Mathematical Imaging and Vision 5: 337–358.
Coif man, R. R. & Wickerhauser, M. V. (1992). Entropy-based algorithms for best basis
selection, IEEE Transacti ons on Information Theory 38: 713 – 718.
Denecker, K., Assche, S. V., Phillips, W. & Lemahieu, I. (1997). State of the art concerning
lossless medical image coding, PRORISC IEEE Benelux Workshop on Circuits,
Syste ms and Signal Process ing, pp. 129–136.
Fernández, G., Periaswamy, S. & Sweldens, W. (1996). LIFTPACK: A software package for
wavelet transforms using lifting, Proceedings of the SPIE - Wavelet Applications in
Signal and Image Proc essing IV, pp. 396–408.
Ferreira, C. B. R. & Borges, D. L. (2001). Automated mammogr am classification using
a multiresolution pattern recognition approach, Proceedings of XIV Brazilian
Symposium on Computer Grap hics and Image Processing, pp. 76 – 83.
Fukunaga, K. & Hayes, R. R. (1989). Effects of sample size in classifier de sign, IEEE Transactions
on Pattern Analysis and Machine Intelligence 11(8): 873 – 885.
Given Imaging Ltd. (2006a). Patient Brochure, World Wid e Web.
http://www.givenimaging.com/Cultures /en-US /Given /English/Professionals/.
Given Imaging Ltd. (2006b). Patient Information Guide, World Wide Web.
http://www.givenimaging.com/Cultures/en-US/Given/English/Patients/.
Given Imaging Ltd. (2006c). PillCam
TM
SB Capsule Endoscopy - Product Information Guide, World
Wide Web. http://www.givenimaging.com/Cultures /en-US /Given/English
/Products/CapsuleEndoscopy/.
Goldbaum, M. (2002). STARE - STructured Analysis of the Retina, World Wide Web.
http://www.parl.clemson.edu/stare/.
Guliato, D., Rangayyan, R. M., de Carvalho, J. D. & Santiago, S. A. (2007). Polygonal
modeling of contours of breast tumors with the preservation of spicules, IEEE Trans.
on Biomedical Engineering .
Haijiang, T., Sei-Ichiro, K., Kazuyuki, T. & Masa- Aki, K. (2004). Lossless image com pression
via multi-scanning and adaptive linear prediction, Vol. 1, The 2004 IEEE Asia-Pacific
Conference on Circuits and System s, pp. 81–84.
Julesz, B. (1981). Textons, the elements of texture perception, and their interactions, Nature
290(5802): 91–97.
Khademi, A. (2006). Multiresolutional analysis for classi�cation and compression of medical images,
Master’s thesis. Ryerson Univers ity, Canada.
Khademi, A. & Krishnan, S. (2006). Multiresolution analysis and classification of small bowel
medical images, Proceedings of IEEE Engineering in Medicine and Biology, pp. 4524
– 4527.
Khademi, A. & Kr ishnan, S. (2007). Shift-invariant discrete wavelet transform anal ysis for
retinal image classification, Journal of Medical and Biological Engineering and Computing
pp. 1–12. in press - online first.
Khademi, A. & Krishnan, S. (2008). Medi cal image texture analysis: A case study with small
bowel, retinal and mammogram images, IEEE CCECE, pp. 1–6.
Kim, B., Park, S., Jee, C. & Yoon, S. (2005). An earthworm-like locomotive mechanism for
capsule endoscopes, IEEE/RSJ International Conference on Intelligent Robots and
Systems, pp. 2997 – 3002.
Lawson, S. & Zhu, J. (2004). Imag e compressio n using wavelets and JPEG2000: a tutorial,
Electronics & Communication Engineering Journal 14(3): 112–121.
Lee, J. K. T. (2007). Interpretation accuracy and pertinence, American College of Radiology
4: 162–165.
Leung, M. M. & Peterso n, A. M. (1992). Scale and rotation i nvariant texture classi fication,
Vol. 1, Conference Record of The Twenty-Sixth Asilomar Conference on Signals,
Systems and Computers, pp. 461 – 465.
Liang, J. & Parks, T. W. (1994). A two-dime nsional tr anslation invariant wavelet representation
and its applications, Vol. 1, IEEE International Conference on Image Processing,
pp. 66 – 70.
Liang, J. & Parks, T. W. (1996). Translation invariant wavelet transforms with symmetric
extensions, IEEE Digital Signal Processing Workshop pp. 69–72.
Liang, J. & Parks, T. W. (1998). Image coding us ing translation invar iant wavelet transforms
with symmetric extensions, IEEE Transactions on Image Processing 7: 762 – 769.
Mallat, S. (1989). A theory for multiresolution signal decomposition: The wavelet
representation, IEEE Transactions on Pattern Analysis and Machine Intelligence
11(7): 674–693.
Mallat, S. (1998). Wavelet Tour of Signal Processing, Academic Press, USA.
Mallat, S. G. & Zhang, Z. (1993). Matching pursuits with time- frequency dictionaries, IEEE
Transactions on Signal Processing 41: 3397 – 3415.
Maragos, P., Mersereau, R. & Shafer, R. (1984). Two-dimensional l inear prediction and its
application to adaptive predictive coding of images, IEEE Transactions on Acoustics,
Speech, and Signal Processing 32: 1213–1229.
Marcellin, M. W., Bilgin, A., Gormish, M. J. & Boliek, M. P. (2000). An overview of JPEG-2000,
Proceedings of the IEEE Data Compression Conference, IEEE Computer Socie ty, p. 523.
Mudigonda, N., Rangayyan, R. & Desautels, J. (2000). Gradient and texture analysis f or
the classification of mammographic masses, IEEE Transactions on Medical Imaging
19(10): 1032–1043.
Rangayyan, R. (2005). Biomedical Image Analysis, CRC Press LLC, United States of America.
Rangay yan, R. M., El -Faramawy, N. M., D esautel s, J. E. L. & Alim, O. (1997). Measures of
acutance and shape for classification of breast tumors, IEEE Transactions on Medical
Imaging 16(6): 799 – 810.
Ross , S. (2003). Introduction to Probability Models, Academic Press , USA, California.
Sato, T., Abe, N., Tanaka, K., Kinoshita, Y. & He, S. (2006). Toward develo ping multiple
organs and diseases d iagnosing intellectual system referring to knowledge base and
ct images, IEEE Symposium on Computer-Based Medical System, pp. 1–6.
Simoncelli, E. P., Freeman, W. T., Adelson, E. H. & Heeger, D. J. (1992). Shiftable multiscale
transforms , IEEE Transactions on Inf ormation Theory 38: 587 – 607.
Sinthanayothin, C., Kongbunkiat, V., Phoo jaruenchanachai, S. & Singalavanija, A. (2003).
Automated screening system for diabetic re tinopathy, Vo l. 2, Proc eedi ngs of the 3rd
International Symposium on Image and Signal Proce ssing and Analysis, pp. 915 –
920.
211
Shift-Invariant DWT for Medical Image Classification
Sweldens, W. (1995). The lifting scheme: A new philosophy in biorthogonal wavelet
constructions, in A. F. Laine & M. Unser (eds), Wavelet Appl ications in S ignal and Image
Processing III, Proc. SPIE
∼2569, pp. 68–79.
Sweldens, W. (1996). Wavelets and the lifting scheme: A 5 minute tour, Z . Angew. Math. Mech.
76 (S uppl. 2): 41–44.
Umbaugh, S. E., Wei, Y. S. & Zuke, M. (1997). Feature extraction in image analysis. a program
for facilitating data reduction in medical image classification, IEEE Engineering in
Medicine and Biology Magazine 16: 62–73.
Vetterli, M. & H erley, C. (1992). Wavelets and filter banks: theory and de sign, IEEE Transactions
on Signal Processing 40(9): 2207 – 2232.
Voulgaris, G. & Jiang, J. (2001). Texture-based im age retriev al in wavelets compressed domain,
Vol. 2, International Conference on Image Processing, pp. 125 – 128.
Wang, H., Hsu, W., Goh, K. & Lee , M. (2000). An effective approach to detect lesions in
color retinal images, Vol. 2, Proceedings of IEEE Conference on Computer Vision and
Pattern Recognition, pp. 181–186.
Wang, T. C. & Karayiannis, N. B. (1998). Detection of microcalcifications in digital
mammograms using wavelets, IEEE Transactio ns on Medical Imaging 17: 498 – 509.
Wei, D., Chan, H. P., Helvie, M. A., Sahiner, B., Petrick, N., Adler, D. D. & Goodsitt, M. M.
(1995). Classification of mass and normal breast tissue on digital mammograms:
multiresolution texture analysis, Medical Physics 22(9): 1501–1513.
Xiong, Z. & Huang, T. S. (2002). Wavelet-based tex ture features can be extracted
efficiently from compressed-domain for JPEG2000 coded images, Vol. 1, International
Confe rence on Image Processing, pp. 481–484.
Zhang, H. & Fritts, J. (2004). An overview of JPEG-2000, Proceedings of SPIE - Visual
Communications and Image Proce ssing, pp. 1333–1340.
Zhang, Y. & Zeytinoglu, M. (1999). Improved lifting schem e for block subband coding,
IEEE Pacific Rim Conference on Communi cations, Computers and Signal Proc essing,
pp. 487 – 490.
212
Discrete Wavelet Transforms - Theory and Applications
Part 4
Industrial Applications
0
Discrete Wavelet Transforms for Synchronization
of Power Converters Connected to Electrical Grids
Albert o Pigazo and Víctor M. Moreno
University of Cantabria
Spain
1. Introduction
Electronic power converters connected to electrical grids allow industrial processes, traction
applications and home appliances to be improved by controlling the energy flow depending
on the operation conditions of both the electrical load and the grid. This is the case of variable
frequency drives, which can be found in pump drives or ship propulsion systems (Bose, 2009)
maintaining the electrical machine in the required operation state while ensuring a proper
current consumption from the electrical grid. Recent researching and developing efforts on
grid-connected power converters are due to the integration of renewable energy sources
in electrical grids, which requires the implementation of new functionalities, such as grid
support, while maintaining reduced current distortion levels and an optimal power extraction
from the renewable energy source (Carrasco et al., 2006; Liserre et al., 2010).
In the most general case, a grid-connected power converter consists of power and control
stage s which ensures the ap propriate energy management (Eri ckson & Maksimovic, 2001;
Mohan et al., 2003). In the first one, electronic power devices, such as power diodes, thyristors,
insulated gate bip olar transistors (IGBTs) or MOS-c ontrolled thyristors (MCTs), and passive
elements (inductances and capacitors) are found . The switching state of the power devices
allows the voltage or/and current across the passive components to be controlled. Resistive
behaviors must be minimized in order to avoid conduction power losses. The second stage,
in case of controlled semiconductor devices, consists of a signal conditioning system and the
required hardware for im plementation o f the converter controller (Bose, 2006).
Recent advances in field p rogrammable gate arrays (FPGAs) and digi tal signal processors
(DSPs) allow the complexity and functionalities of the controllers employed in power
converters to be increase d and improved (Bueno et al., 2009). In grid-connected power
converters these functionalities include, in m ost cases, the synchronization with the electrical
grid, the evaluation of the reference current amplitude at the grid-side and current control
(Kazmierkow ski et al., 2002). The amplitude and phase of the grid-side current depends
on the reference current evaluation and the synchronization subsystems while the current
controller ensures that the current waveform matches the reference o ne. The implementation
of these subsystems depends on the application char acteristics. Other functional ities, such as
grid support (Ullah et al., 2009) or detection of the islanding condition (De Mango, Lis erre &
D’Aquila, 2006; De Mango, Liserre, D’Aquila & Pigazo, 2006), can be added if it is required.
These controller functionalities can be implemented by applying diverse approaches, such as
digital sig nal processing techniques, i .e. Four ier Transfo rms (McGrath e t al., 2005), Kalm an
11
Filters (Moreno et al., 2007) or Discrete Wavelet Tr ansforms (DWTs) (Pigazo et al., 2009).
Frequency and time localization of wavelet analysis allow the performance of controllers in
grid-connected power converters to be improved. This is the case of active power filters, where
the compensation reference curre nt can be evaluated by means of DWT (Driesen & Belmans,
2002), modulation techniques in controlled rectifiers (Saleh & Rahman, 2009) or the controller
design process using averaging models of power converters (Gandelli et al., 2001).
This book chapter pro poses to take advantage of DWTs’ properties in order to impro ve the
synchronization subsystem of controllers in g rid-connected power converters. After a review
of the state of art in wavelet analysis applied to power e lectronics, the main characteristics
of controllers in grid-connected power converters are presented as well as the new approach
for sy nchronization purposes. Results validating the proposal, considering diverse operation
conditions, are shown.
2. Wavelet analysis applied to power converters
The wavelet analysis has been mainly applied to signal analysis and processing (i.e.
identification and classification) in electrical power systems (voltage and current) du ring
the last twenty years (Ribeiro, 1994; Robertson et al., 1994). The wavelet analysis was firstly
applied to power system protection, power quality measurement, detection of power system
transients, partial discharges, forecasting of electrical loads due to its its capability for fast
and accurate ide ntification of transients (Castro & Diaz, 2002). In recent years this signal
processing technique has been also applied in order to control power electronic converters,
such as dc-dc, inverters, rectifiers, active power filters and unified power quality conditioners
(UPQCs). This chapter section shows some of these applications both to power systems and,
more specifically, power converters.
2.1 Wavelet analysis in power systems
The power system protection can be i mproved by applying the wavelet analysis to activate the
relays in case of power system transients. Time resolution capability of the wavelet analysis
is employed in (Chaari et al., 1996) for detection of earth faults in case of a 20 kV resonant
grounded network. High impedance faults identification and protection of transformer s and
generators by means of wavelets are also s hown in (Solanki et al., 2001) and (Eren & Dev aney,
2001) respectively. In this last cas e, the frequency resolution of wavel ets allows the changes of
the power signals’ spectra to be measured in order to dete ct the degradation of the i nsulatio n
and identify internal and external faults. Wavelets have been also employed for modeling of
electrical machines in wind turbines and detection of turn-to-turn rotor faults (Dinkhauser &
Fuchs, 2008).
The evaluation of the electrical power quality (PQ) can take advantage of wavelet analysis
for detection and measurement of interferences, impulses, notches, glitches, interruptions,
harmonics, flicker and other disturbances. In case of harmonic currents/vo ltages and voltage
flicker the multiresolution analysis (MRA) using wavelet fil ter banks (Pham & Wong, 1999;
Pham et al., 2000) and continuous w avelet transforms (Zhen et al., 2000) can be applied. The
propagation of power s ystem transie nts can be also analyzed by means of wavelets (Heydt &
Galli, 1997; Wilkinson & Cox, 1996). The characteris tics of partial d ischarges (short duratio n,
high frequency and low amplitude) make it difficult to detect. Wavelet analysis allows partial
discharges to be detected due to its time resolution, as it is shown in (Shim et al., 2000) in case
of transformer windings and cables.
216
Discrete Wavelet Transforms - Theory and Applications
Filters (Moreno et al., 2007) or Discrete Wavelet Tr ansforms (DWTs) (Pigazo et al., 2009).
Frequency and time localization of wavelet analysis allow the performance of controllers in
grid-connected power converters to be improved. This is the case of active power filters, where
the compensation reference curre nt can be evaluated by means of DWT (Driesen & Belmans,
2002), modulation techniques in controlled rectifiers (Saleh & Rahman, 2009) or the controller
design process using averaging models of power converters (Gandelli et al., 2001).
This book chapter pro poses to take advantage of DWTs’ properties in order to impro ve the
synchronization subsystem of controllers in g rid-connected power converters. After a review
of the state of art in wavelet analysis applied to power e lectronics, the main characteristics
of controllers in grid-connected power converters are presented as well as the new approach
for sy nchronization purposes. Results validating the proposal, considering diverse operation
conditions, are shown.
2. Wavelet analysis applied to power converters
The wavelet analysis has been mainly applied to signal analysis and processing (i.e.
identification and classification) in electrical power systems (voltage and current) du ring
the last twenty years (Ribeiro, 1994; Robertson et al., 1994). The wavelet analysis was firstly
applied to power system protection, power quality measurement, detection of power system
transients, partial discharges, forecasting of electrical loads due to its its capability for fast
and accurate ide ntification of transients (Castro & Diaz, 2002). In recent years this signal
processing technique has been also applied in order to control power electronic converters,
such as dc-dc, inverters, rectifiers, active power filters and unified power quality conditioners
(UPQCs). This chapter section shows some of these applications both to power systems and,
more specifically, power converters.
2.1 Wavelet analysis in power systems
The power system protection can be i mproved by applying the wavelet analysis to activate the
relays in case of power system transients. Time resolution capability of the wavelet analysis
is employed in (Chaari et al., 1996) for detection of earth faults in case of a 20 kV resonant
grounded network. High impedance faults identification and protection of transformer s and
generators by means of wavelets are also s hown in (Solanki et al., 2001) and (Eren & Dev aney,
2001) respectively. In this last cas e, the frequency resolution of wavel ets allows the changes of
the power signals’ spectra to be measured in order to dete ct the degradation of the i nsulatio n
and identify internal and external faults. Wavelets have been also employed for modeling of
electrical machines in wind turbines and detection of turn-to-turn rotor faults (Dinkhauser &
Fuchs, 2008).
The evaluation of the electrical power quality (PQ) can take advantage of wavelet analysis
for detection and measurement of interferences, impulses, notches, glitches, interruptions,
harmonics, flicker and other disturbances. In case of harmonic currents/vo ltages and voltage
flicker the multiresolution analysis (MRA) using wavelet fil ter banks (Pham & Wong, 1999;
Pham et al., 2000) and continuous w avelet transforms (Zhen et al., 2000) can be applied. The
propagation of power s ystem transie nts can be also analyzed by means of wavelets (Heydt &
Galli, 1997; Wilkinson & Cox, 1996). The characteris tics of partial d ischarges (short duratio n,
high frequency and low amplitude) make it difficult to detect. Wavelet analysis allows partial
discharges to be detected due to its time resolution, as it is shown in (Shim et al., 2000) in case
of transformer windings and cables.
The efficient management of electrical power system requires a proper forecasting of electrical
loads. The combinatio n of wavelets and neural networks in (Huang & Yang, 2001; Yao et al.,
2000) allows it by considering the current waveforms as a linear combination of different
frequencies. The wavelet analysis can also be applied for measurement of the electrical
active/reactive power and the root mean square (rms) value of line voltages and currents
on a frequency band basi s (Hami d & Kawasaki, 2001) .
2.2 Wavelet analysis in controllers for power converters
Wavelets have been recently applied in power converters used in diverse applications. The
covered functionalities include modeling of the power converter, its control and supervision
tasks.
In order to obtain a more flexible model of a dc/dc power converter, wavelets are applied in
(Ponci et al., 2009) for detection of the operation mode of the power converter, consisting on
an extension of conventional analysis techniques based on state-space averaging. A model of
a dc/ac converter based on wavelets i s obtained in (Gandelli et al., 2002) in order to perfor m
a detailed analysis and the optim ization of the power converter.
Wavelet-based controllers have been also proposed in literature in order to improve the
performance of the power converter. This is the case of (Hsu et al., 2008), where a
wavelet-based neural network is employed in order to minimize the impact of input voltage
and load resistance variations on a dc/dc converter. In (Saleh & Rahm an, 2009) wavelets allow
a new switching strategy to be developed in order to reduce the harmonic content of the
output voltage in a ac/dc converter maintaining unity power factor. A three-phase induction
generator (IG) system for stand-alone power systems is controlled by means of one ac/dc plus
one dc/ac converter and applying a recurrent wavelet neural netwo rk (RWNN) controller
with improved particle sw arm opti mization (IPSO) (Teng et al., 2009). The controllers in
dc/ac converters can be opti mized by applying wavelets, this is the case of (Mercorelli et al.,
2004), where it is employed for optimization of the applied model predictive controller. The
wavelet analysis is applied in (González et al., 2008) in order to evaluate the performance of
the employed modulation technique, incl uding the spec trum of the converter output voltage
and its ripple. Controllers in multilevel converters can also take advantage of wavelets, as it
is shown in (Iwaszkiewicz & Perz, 2007), in order to ensure a better and faster adaptation of
their output voltage waveforms to sine waveforms and reduce the harmonic distortion of the
output voltage at relatively low switching frequencies. High-level control functionalities, such
as islanding detection or source impedance measurement, required in distributed generation
systems connected to electrical grid s can also obtain benefits from the wavelet analysis. The
high frequency bands of voltage and current waveforms are evaluated in (Pi gazo et al. ,
2009; 2007) in order to dete ct the islanding condition. The power sys tem impedance can
be measured in real-time by injecting a controlled disturbance into the electrical grid, the
wavelet analysis allows an fast detection of faults (Sumner et al., 2006).The wavelets can be
also applied for characterization of power converters’ performance. In (Kneze vic et al., 2000)
the wavelet analysis is applied for measurement of transients caused by ac/dc converters.
3. Controllers in grid-connected power converters
The general structure of a single-phase grid-connected power converter, including both power
and control stages, is shown in Fi g. 1. The power stage of the dc/ac converter consists o f an
IGBT full-bridge with d iodes, which synthesizes a low frequency ac voltage by changing the
IGBTs’ swi tching states, the gate circuit, whic h applies the required gate signals in order to
217
Discrete Wavelet Transforms for Synchronization
of Power Converters Connected to Electrical Grids
switch on and off the controlled power devices, an LCL-filter, employed as a second-order low
pass filtering stage which allows the high freq uency ripple of the full-bridge output voltage to
be filtered out and a dc-side filtering stage, which can be implemented by means of one shunt
capacitor (first order) or a series inductance plus a shunt capacitor (second ord er).
dc
load or bus
R
L
2
1
R
3
L
2
R
1
C
3
LCL filter with damping
single-phase grid-connected power converter
PWM
current
controller
grid
synchronization
digital
controller
i
sin t
g
Reference
Current
Evaluation
v
g
gate circuit
IGBT
H-bridge
C
dc
+
dc-side
filter
i
*
v
g
acquisition
signal
conditioning
acquisition
signal
conditioning
i
g
Fig. 1. Three-phases three-wires grid connected dc/ac converter.
Depending on the application characteristics, the converter controller functionalities are
implemented using analog or digital circuitries and, in the second case, FPGAs, DPSs
and microcontrollers (μCs) allow more flexible and complex controllers to be designed
and implemented (Bueno et al., 2008; Koizumi et al., 2006; Kojabadi et al., 2006).
In case of grid-connected power converters, both inverters and controlled rectifiers
switching at relatively high frequencies (around 10 kHz), the main functionalities that
must be implemented are grid s ynchronizati on, evaluation of the reference for current
injection/consumption, grid side cu rrent control and pulse width modulation ( PWM)
(Kazmierkow ski et al., 2002). The grid synchronization block must generate, at least, a
reference signal sin ωt which must track properly the fundamental component of the grid
voltage v
g
. Depending on the application, i.e. distributed generation systems, the grid
frequency must be also measured in order to implement load sharing algorithms (Guerrero
et al., 2004). The evaluation of the instantaneous values of the reference current i
∗
is required
in order to determine the proper current which must flow from/to the electrical grid i
g
.
The implementation of this functionality depends on the applicati on and, hence, on the
implemented high level control functionalities such as reactive power requirements, harmonic
control, tolerance to grid disturbances or the maintenance of the dc-bus voltage. The obtained
values of i
∗
are applied to a current controller. This block must ensure that the grid side current
i
g
matches the reference ones i
∗
. Div erse approaches, such as hysteresis (Ho et al., 2009),
dead beat (Mohamed & El-Saadany, 2008), p ropor tional-integral (PI) control lers (Dannehl
et al., 2010), resonant controllers (Liserre et al., 2006), repetitive controllers (Weiss et al., 2004)
or inne r model controllers (Gabe et al., 2009), c an be found in literature for this purpose.
218
Discrete Wavelet Transforms - Theory and Applications