184 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 37, NO. 1, JANUARY/FEBRUARY 2001 Wavelet and Neural Structure: A New Tool for Diagnostic of Power System Disturbances Dolores Borrás, M. Castilla, Member, IEEE, Narciso Moreno, and J. C. Montaño, Senior Member, IEEE Abstract—The Fourier transform can be used for analysis of nonstationary signals, but the Fourier spectrum does not provide any time-domain information about the signal. When the time lo- calization of the spectral components is needed, a wavelet trans- form giving the time-frequency representation of the signal must be used. In this paper, using wavelet analysis and neural systems as a new tool for the analysis of power system disturbances, distur- bances are automatically detected, compacted, and classified. An example showing the potential of these techniques for diagnosis of actual power system disturbances is presented. Index Terms—Harmonic distortion, neural networks, signal analysis, transforms, wavelets. I. INTRODUCTION I N ORDER to determine the sources and causes of harmonic distortion of the voltage signal delivered by utilities, one must be able to detect and localize those disturbances and clas- sify the different types. Software procedures applying the fast Fourier transform (FFT) have been developed for this purpose [1], but due to the great amount of stored data and the time re- quired for processing, such procedure is slow and not very effi- cient. Continuous and discrete wavelet transforms (CWTs and DWTs) have been used in analysis of nonstationary signals, and several recent papers, such as [2] and [3], have proposed the use of wavelets for power systems analysis. Wavelet transforms are mathematical tools with powerful structure and enormous freedom that decompose a given signal into several scales at different levels of resolution. At each scale, the WT coefficients corresponding to a given disturbance are larger than those not corresponding to such disturbance. Thus, related coefficients are kept, while others not related to the disturbance are dis- carded. As a consequence, data could be reduced considerably in number with very little loss of information. Paper TE 00–151, presented at the 1999 IEEE International Symposium on Diagnostics for Electrical Machines Power Electronics and Drives, Asturias, Spain, September 1–3, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Power Systems Engineering Committee of the IEEE Industry Applications Society. Manuscript submitted for review Feb- ruary 15, 2000 and released for publication September 14, 2000. This work was supported by the Spanish Ministerio de Educación y Cultura under Project CICYT: TIC97-1221-C02-01 and the Consejería de Educación y Ciencia (Di- rección General de Universidades e Investigación) of the Junta de Andalucía (Spain). D. Borrás, M. Castilla, and N. Moreno are with the Department of Elec- trical Engineering, Universidad de Sevilla, 41011 Seville, Spain (e-mail: borras@platero.eup.us.es; castilla@cica.es; narciso@cica.es). J. C. Montaño is with Consejo Superior de Investigaciones Científicas, Seville, Spain (e-mail: montano@irnase.csic.es). Publisher Item Identifier S 0093-9994(01)00889-1. In this work, a WT approach is proposed to detect and classify various types of power systems disturbance. The method selects the most suitable type of wavelet and applies the DWT. The re- construction process is thereby obtained both with and without the disturbed signal, using a reduced number of coefficients. The algorithm of coefficient filtering to compress the signal is based on the procedures described in [4]. A neural network structure may be used to classify typical disturbances found in power sys- tems. Definitions and concepts of WT are introduced in Section II. The proposed method is described in Section III-A. Finally, re- sults of simulation are given in Section III-B and conclusions in Section IV. II. WAVELET THEORY Wavelets are functions that satisfy certain mathematical re- quirements and are used in representing data or other functions. This idea is not new. Approximation using superposition of functions has existed since the early 19th century with Fourier analysis. The Fourier transform (FT) uses basis functions (sines and cosines) to analyze and reconstruct a function. The wavelet approach is more suitable than the Fourier one, especially when signals are nonstationary. Wavelet algorithms process data at different scale or resolution. In wavelet analysis, the scale that we use to look at data plays a special role. A basis function varies in scale by chopping up the same function or data space using different scale sizes. Various wavelets are obtained from a single wavelet (mother wavelet) by scaling and shifting operations. A signal or function can often be better analyzed or pro- cessed if expressed as a linear decomposition by (1) where is an integer index, are the real coefficients, and is a set of functions if the expansion (1) is unique. If the basis is orthogonal, it should also satisfy (2) where is the inner product. For the wavelet expansion, (1) is expressed as (3) 0093–9994/01$10.00 © 2001 IEEE