Skip to content


  • Research Article
  • Open Access

Modeling of Electric Disturbance Signals Using Damped Sinusoids via Atomic Decompositions and Its Applications

  • 1Email author,
  • 2, 3,
  • 2,
  • 3 and
  • 2
EURASIP Journal on Advances in Signal Processing20072007:029507

  • Received: 10 August 2006
  • Accepted: 17 December 2006
  • Published:


The number of waveforms monitored in power systems is increasing rapidly. This creates a demand for computational tools that aid in the analysis of the phenomena and also that allow efficient transmission and storage of the information acquired. In this context, signal processing techniques play a fundamental role. This work is a tutorial reviewing the principles and applications of atomic signal modeling of electric disturbance signals. The disturbance signal is modeled using a linear combination of damped sinusoidal components which are closely related to the phenomena typically observed in power systems. The signal model obtained is then employed for disturbance signal denoising, filtering of "DC components," and compression.


  • Information Technology
  • Linear Combination
  • Signal Processing
  • Power System
  • Quantum Information


Authors’ Affiliations

Departamento de Eletrônica e Telecomunicações (DETEL), Faculdade de Engenharia (FEN), Universidade do Estado do Rio de Janeiro (UERJ), Rio de Janeiro, RJ, 20550-900, Brazil
Laboratory of Signal Processing, PEE/COPPE and DEL/Poli, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, CP 68504, 21941-972, Brazil
Electric Power Research Center (CEPEL), Rio de Janeiro, RJ, CP 68007, 21941-590, Brazil


  1. Rodrigues MAM, de Figueiredo MVF, Miranda ALL, Diniz SS: Oscillography for power system operational planning. Proceedings of the 7th Symposium of Specialists in Electric Operational and Expansion Planning (VII SEPOPE '00), May 2000, Curitiba, BrazilGoogle Scholar
  2. Arrillaga J, Bollen MHJ, Watson NR: Power quality following deregulation. Proceedings of the IEEE 2000,88(2):246-261. 10.1109/5.824002View ArticleGoogle Scholar
  3. Dugan RC, McGranghan MF, Beaty HW: Electrial Power Systems Quality. McGraw-Hill, New York, NY, USA; 1996.Google Scholar
  4. Bollen MHJ: Understanding Power Quality Problems—Voltage Sags and Interruptions. IEEE Press, Piscataway, NJ, USA; 2000.Google Scholar
  5. Ruiz-Reyes N, Vera-Candeas P, Jurado F: Discrimination between transient voltage stability and voltage sag using damped sinusoids-based transient modeling. IEEE Transactions on Power Delivery 2005,20(4):2644-2650. 10.1109/TPWRD.2005.855436View ArticleGoogle Scholar
  6. Kezunovic M, Rikalo I: Automating the analysis of faults and power quality. IEEE Computer Applications in Power 1999,12(1):46-50. 10.1109/67.738319View ArticleGoogle Scholar
  7. Bujanowski BJ, Pierre JW, Hietpas SM, Sharpe TL, Pierre DA: A comparison of several system identification methods with application to power systems. Proceedings of the 36th Midwest Symposium on Circuits and Systems (MWSCAS '93), August 1993, Detroit, Mich, USA 1: 64-67.View ArticleGoogle Scholar
  8. Ibrahim WRA, Morcos MM: Artificial intelligence and advanced mathematical tools for power quality applications: a survey. IEEE Transactions on Power Delivery 2002,17(2):668-673. 10.1109/61.997958View ArticleGoogle Scholar
  9. Schweitzer EO III, Hou D: Filtering for protective relays. Proceedings of the 47th Annual Georgia Tech Protective Relaying Conference, April 1993, Atlanta, Ga, USAGoogle Scholar
  10. Wiot D: A new adaptive transient monitoring scheme for detection of power system events. IEEE Transactions on Power Delivery 2004,19(1):42-48. 10.1109/TPWRD.2003.820416View ArticleGoogle Scholar
  11. Lobos T, Rezmer J, Koglin H-J: Analysis of power system transients using wavelets and Prony method. Proceedings of IEEE Porto Power Tech Conference (PTC '01), September 2001, Porto, Portugal 4: 4.Google Scholar
  12. Tawfik MM, Morcos MM: ANN-based techniques for estimating fault location on transmission lines using Prony method. IEEE Transactions on Power Delivery 2001,16(2):219-224. 10.1109/61.915486View ArticleGoogle Scholar
  13. Galli AW, Heydt GT, Ribeiro PF: Exploring the power of wavelet analysis. IEEE Computer Applications in Power 1996,9(4):37-41. 10.1109/67.539845View ArticleGoogle Scholar
  14. Chung J, Powers EJ, Grady WM, Bhatt SC: Electric power transient disturbance classification using wavelet-based hidden Markov models. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 6: 3662-3665.Google Scholar
  15. Pillaya P, Bhattacharjee A: Application of wavelets to model short-term power system disturbances. IEEE Transactions on Power Systems 1996,11(4):2031-2037. 10.1109/59.544681View ArticleGoogle Scholar
  16. Poisson O, Rioual P, Meunier M: Detection and measurement of power quality disturbances using wavelet transform. IEEE Transactions on Power Delivery 2000,15(3):1039-1044. 10.1109/61.871372View ArticleGoogle Scholar
  17. Yang H-T, Liao C-C: A de-noising scheme for enhancing wavelet-based power quality monitoring system. IEEE Transactions on Power Delivery 2001,16(3):353-360. 10.1109/61.924810MathSciNetView ArticleGoogle Scholar
  18. Santoso S, Grady WM, Powers EJ, Lamoree J, Bhatt SC: Characterization of distribution power quality events with Fourier and wavelet transforms. IEEE Transactions on Power Delivery 2000,15(1):247-254. 10.1109/61.847259View ArticleGoogle Scholar
  19. Karimi M, Mokhtari H, Iravani MR: Wavelet based on-line disturbance detection for power quality applications. IEEE Transactions on Power Delivery 2000,15(4):1212-1220. 10.1109/61.891505View ArticleGoogle Scholar
  20. Duque CA, Ribeiro MV, Ramos FR, Szczupak J: Power quality event detection based on the divide and conquer principle and innovation concept. IEEE Transactions on Power Delivery 2005,20(4):2361-2369. 10.1109/TPWRD.2005.855478View ArticleGoogle Scholar
  21. Ribeiro MV, Romano JMT, Duque CA: An improved method for signal processing and compression in power quality evaluation. IEEE Transactions on Power Delivery 2004,19(2):464-471. 10.1109/TPWRD.2003.822497View ArticleGoogle Scholar
  22. Lovisolo L, da Silva EAB, Rodrigues MAM, Diniz PSR: Efficient coherent adaptive representations of monitored electric signals in power systems using damped sinusoids. IEEE Transactions on Signal Processing 2005,53(10 I):3831-3846.MathSciNetView ArticleGoogle Scholar
  23. Karimi-Ghartemani M, Iravani MR: A signal processing module for power system applications. IEEE Transactions on Power Delivery 2003,18(4):1118-1126. 10.1109/TPWRD.2003.817514View ArticleGoogle Scholar
  24. Mallat S, Zhang Z: Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing 1993,41(12):3397-3415. 10.1109/78.258082View ArticleMATHGoogle Scholar
  25. Mallat S: A Wavelet Tour of Signal Processing. 1st edition. Academic Press, San Diego, Calif, USA; 1998.MATHGoogle Scholar
  26. Ferrando SE, Kolasa LA, Kovačević N: Algorithm 820: a flexible implementation of matching pursuit for Gabor functions on the interval. ACM Transactions on Mathematical Software 2002,28(3):337-353. 10.1145/569147.569151View ArticleMATHGoogle Scholar
  27. Goodwin MM, Vetterli M: Matching pursuit and atomic signal models based on recursive filter banks. IEEE Transactions on Signal Processing 1999,47(7):1890-1902. 10.1109/78.771038View ArticleGoogle Scholar
  28. Gribonval R, Bacry E: Harmonic decomposition of audio signals with matching pursuit. IEEE Transactions on Signal Processing 2003,51(1):101-111. 10.1109/TSP.2002.806592MathSciNetView ArticleGoogle Scholar
  29. Xu W: Component modeling issues for power quality assessment. IEEE Power Engineering Review 2001,21(11):12-15, 17.View ArticleGoogle Scholar
  30. Collins JJ, Hurley WG: Application of expert systems and neural networks to the diagnosis of power quality problems. Proceedings of the EPRI-PQA Conference, October 1994, Amsterdam, The NetherlandsGoogle Scholar
  31. Ghosh AK, Lubkeman DL: The classification of power system disturbance waveforms using a neural network approach. IEEE Transactions on Power Delivery 1995,10(1):109-115. 10.1109/61.368408View ArticleGoogle Scholar
  32. Lovisolo L, da Silva EAB, Rodrigues MAM, Diniz PSR: Coherent decompositions of power systems signals using damped sinusoids with applications to denoising. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '02), May 2002, Phoenix, Ariz, USA 5: 685-688.Google Scholar
  33. Rodrigues MAM: Efficient decompositions for signal coding, Ph.D. thesis. COPPE/UFRJ, Rio de Janeiro, RJ, USA; 1999.Google Scholar
  34. Friedlander B, Porat B: Detection of transient signals by the Gabor representation. IEEE Transactions on Acoustics, Speech, and Signal Processing 1989,37(2):169-180. 10.1109/29.21680View ArticleGoogle Scholar
  35. Friedlander B, Zeira A: Oversampled Gabor representation for transient signals. IEEE Transactions on Signal Processing 1995,43(9):2088-2094. 10.1109/78.414770View ArticleGoogle Scholar
  36. Zibulski M, Zeevi YY: Discrete multiwindow Gabor-type transforms. IEEE Transactions on Signal Processing 1997,45(6):1428-1442. 10.1109/78.599955View ArticleMATHGoogle Scholar
  37. Kauppinen I, Kauppinen J, Saarinen P: A method for long extrapolation of audio signals. Journal of the Audio Engineering Society 2001,49(12):1167-1180.Google Scholar
  38. Lu Y, Joshi S, Morris JM: Noise reduction for NMR FID signals via Gabor expansion. IEEE Transactions on Biomedical Engineering 1997,44(6):512-528. 10.1109/10.581949View ArticleGoogle Scholar
  39. Kay SM: Modern Spectral Estimation. Prentice-Hall, Englewood Cliffs, NJ, USA; 1988.MATHGoogle Scholar
  40. Tufts DW, Kumaresan R: Improved spectral resolution. Proceedings of the IEEE 1980,68(3):419-421.View ArticleGoogle Scholar
  41. Abatzoglou TJ: A fast maximum likelihood algorithm for frequency estimation of a sinusoid based on Newton's method. IEEE Transactions on Acoustics, Speech, and Signal Processing 1985,33(1):77-89. 10.1109/TASSP.1985.1164541View ArticleMATHGoogle Scholar
  42. Kumaresan R, Tufts DW: Estimating the parameters of exponentially damped sinusoids and pole-zero modeling in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing 1982,30(6):833-840. 10.1109/TASSP.1982.1163974View ArticleGoogle Scholar
  43. Hua Y, Sarkar TK: Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing 1990,38(5):814-824. 10.1109/29.56027MathSciNetView ArticleMATHGoogle Scholar
  44. Papadopoulos CK, Nikias CL: Parameter estimation of exponentially damped sinusoids using higher order statistics. IEEE Transactions on Acoustics, Speech, and Signal Processing 1990,38(8):1424-1436. 10.1109/29.57577View ArticleGoogle Scholar
  45. Hua Y: Parameter estimation of exponentially damped sinusoids using higher order statistics and matrix pencil. IEEE Transactions on Signal Processing 1991,39(7):1691-1692. 10.1109/78.134411View ArticleGoogle Scholar
  46. Ruiz DP, Carrion MC, Gallego A, Medouri A: Parameter estimation of exponentially damped sinusoids using a higher order correlation-based approach. IEEE Transactions on Signal Processing 1995,43(11):2665-2677. 10.1109/78.482116View ArticleMATHGoogle Scholar
  47. Ribeiro MV, Park SH, Romano JMT, Mitra SK: A novel MDL-based compression method for power quality applications. IEEE Transactions on Power Delivery 2007,22(1):27-36.View ArticleGoogle Scholar
  48. Krim H, Tucker D, Mallat S, Donoho D: On denoising and best signal representation. IEEE Transactions on Information Theory 1999,45(7):2225-2238. 10.1109/18.796365MathSciNetView ArticleMATHGoogle Scholar
  49. Vera-Candeas P, Ruiz-Reyes N, Rosa-Zurera M, Martinez-Muñoz D, Lopez-Ferreras F: Transient modeling by matching pursuits with a wavelet dictionary for parametric audio coding. IEEE Signal Processing Letters 2004,11(3):349-352. 10.1109/LSP.2003.822904View ArticleGoogle Scholar
  50. Heusdens R, Vafin R, Kleijn WB: Sinusoidal modeling using psychoacoustic-adaptive matching pursuits. IEEE Signal Processing Letters 2002,9(8):262-265. 10.1109/LSP.2002.802999View ArticleGoogle Scholar
  51. Jaggi S, Karl WC, Mallat S, Willsky AS: High resolution pursuit for feature extraction. Applied and Computational Harmonic Analysis 1998,5(4):428-449. 10.1006/acha.1997.0239View ArticleMATHGoogle Scholar
  52. Goodwin MM: Adaptive Signal Models: Theory, Algorithms, and Audio Applications, Kluwer International Series in Engineering and Computer Science. 1st edition. Kluwer Academic, New York, NY, USA; 1998.View ArticleGoogle Scholar
  53. Donoho DL, Vetterli M, DeVore RA, Daubechies I: Data compression and harmonic analysis. IEEE Transactions on Information Theory 1998,44(6):2435-2476. 10.1109/18.720544MathSciNetView ArticleMATHGoogle Scholar
  54. Engan K, Aase SO, Husøy JH: Multi-frame compression: theory and design. Signal Processing 2000,80(10):2121-2140. 10.1016/S0165-1684(00)00072-4View ArticleMATHGoogle Scholar
  55. Al-Shaykh OK, Miloslavsky E, Nomura T, Neff R, Zakhor A: Video compression using matching pursuits. IEEE Transactions on Circuits and Systems for Video Technology 1999,9(1):123-143. 10.1109/76.744280View ArticleGoogle Scholar
  56. Neff R, Zakhor A: Modulus quantization for matching-pursuit video coding. IEEE Transactions on Circuits and Systems for Video Technology 2000,10(6):895-912. 10.1109/76.867927View ArticleGoogle Scholar
  57. Caetano R, da Silva EAB, Ciancio AG: Matching pursuits video coding using generalized bit-planes. Proceedings of International Conference on Image Processing (ICIP '02), September 2002, Rochester, NY, USA 3: 677-680.Google Scholar
  58. Gribonval R: From projection pursuit and CART to adaptive discriminant analysis? IEEE Transactions on Neural Networks 2005,16(3):522-532. 10.1109/TNN.2005.844900View ArticleGoogle Scholar
  59. Goyal VK, Vetterli M, Thao NT:Quantized overcomplete expansions in : analysis, synthesis, and algorithms. IEEE Transactions on Information Theory 1998,44(1):16-31. 10.1109/18.650985MathSciNetView ArticleMATHGoogle Scholar
  60. Davis G: Adaptive nonlinear approximations, Ph.D. thesis. New York University, New York, NY, USA; 1994.Google Scholar
  61. Tropp JA: Greed is good: algorithmic results for sparse approximation. IEEE Transactions on Information Theory 2004,50(10):2231-2242. 10.1109/TIT.2004.834793MathSciNetView ArticleMATHGoogle Scholar
  62. Adler J, Rao BD, Kreutz-Delgado K: Comparison of basis selection methods. Proceedings of the 30th Asilomar Conference on Signals Conference on Signals, Systems & Computers (ACSSC '96), November 1997, Pacific Grove, Calif, USA 1: 252-257.View ArticleGoogle Scholar
  63. Zhang Z: Matching pursuits, Ph.D. dissertation. New York University, New York, NY, USA, 1993MATHGoogle Scholar
  64. Kruskal JB: Toward a practical method to hel uncover the structure of a set of multivariate observations by finding the linear transformation which optimizes a new "index of condensation". In Statistical Computation. Edited by: Milton RC, Nelder JA. Academic Press, New York, NY, USA; 1969.Google Scholar
  65. Friedman JH, Suetzle W: Projection pursuit regression. Journal of the American Statiscal Association 1981,76(376):817-823. 10.2307/2287576View ArticleMathSciNetGoogle Scholar
  66. Chen S, Billings SA, Luo W: Orthogonal least squares methods and their application to non-linear system identification. International Journal of Control 1989,50(5):1873-1896. 10.1080/00207178908953472MathSciNetView ArticleMATHGoogle Scholar
  67. DeVore RA: Nonlinear approximation. Acta Numerica 1998, 7: 51-150.MathSciNetView ArticleMATHGoogle Scholar
  68. Temlyakov VN: Nonlinear methods of approximation. Foundations of Computational Mathematics 2003,3(1):33-107. 10.1007/s102080010029MathSciNetView ArticleMATHGoogle Scholar
  69. DeVore RA, Temlyakov VN: Some remarks on greedy algorithms. Advances in Computational Mathematics 1996,5(1):173-187. 10.1007/BF02124742MathSciNetView ArticleMATHGoogle Scholar
  70. Gribonval R, Bacry E, Mallat S, Depalle P, Rodet X: Analysis of sound signals with high resolution matching pursuit. Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (TFTSA '96), June 1996, Paris, France 125-128.View ArticleGoogle Scholar
  71. Frossard P, Vandergheynst P, Figueras I Ventura RM, Kunt M: A posteriori quantization of progressive matching pursuit streams. IEEE Transactions on Signal Processing 2004,52(2):525-535. 10.1109/TSP.2003.821105MathSciNetView ArticleGoogle Scholar
  72. Durka PJ, Ircha D, Blinowska KJ: Stochastic time-frequency dictionaries for matching pursuit. IEEE Transactions on Signal Processing 2001,49(3):507-510. 10.1109/78.905866View ArticleGoogle Scholar
  73. Papandreou-Suppappola A, Suppappola SB: Analysis and classification of time-varying signals with multiple time-frequency structures. IEEE Signal Processing Letters 2002,9(3):92-95. 10.1109/97.995826View ArticleMATHGoogle Scholar
  74. Ferrando SE, Doolittle EJ, Bernal AJ, Bernal LJ: Probabilistic matching pursuit with Gabor dictionaries. Signal Processing 2000,80(10):2099-2120. 10.1016/S0165-1684(00)00071-2View ArticleMATHGoogle Scholar
  75. Daubechies I: Ten Lectures on Wavelets. SIAM, Philadelphia, Pa, USA; 1991.MATHGoogle Scholar
  76. Etemoǧlu CO, Cuperman V: Matching pursuits sinusoidal speech coding. IEEE Transactions on Speech and Audio Processing 2003,11(5):413-424. 10.1109/TSA.2003.815520View ArticleGoogle Scholar
  77. IEEE PES Working Group 1433 Power Quality
  78. Cerqueira AS, Duque CA, Trindade RM, Ribeiro MV: Digital system for detection and classification of electrical events. Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS '05), May 2005, Kobe, Japan 6: 5417-5420.View ArticleGoogle Scholar
  79. Canadian-American EMTP User Group : EMTP Rule Book, Alternative Transients Rule Book . Canadian-American EMTP User Group, 1987–1992Google Scholar
  80. Ortega A, Ramchandran K: Rate-distortion methods for: image and video compression. IEEE Signal Processing Magazine 1998,15(6):23-50. 10.1109/79.733495View ArticleGoogle Scholar
  81. Tcheou MP, Lovisolo L, da Silva EAB, Rodrigues MAM, Diniz PSR: Optimum rate-distortion dictionary selection for compression of atomic decompositions of electric disturbance signals. IEEE Signal Processing Letters 2007,14(2):81-84.View ArticleMATHGoogle Scholar


© Lisandro Lovisolo et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.