**2.1 Wavelet analysis**

178 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

One of the main difficulties in using measurements, obtained by DDR, in the evaluation of power quality as compared with those obtained by power quality monitors, is that many of the signal processing stages are not performed automatically by the first. For the oscillographic records to be useful as power quality indicators, it is first necessary to obtain certain parameters to classify the recorded signals according to the event type that has occurred. Considering the case of short duration voltage variations (SDVV), the parameters of interest are the event amplitude and time duration. Obtaining these parameters enables the application of statistical tools as presented in (Bollen, 2000), for results analysis and visualization, which allows having information about the electrical system behavior at

Another difficulty, perhaps the most critical, is the large volume of data obtained from oscillographic monitoring. Many of these recorded signals are due to switching maneuvers, or due to spurious signals or noise, without characterizing voltage changes in the electrical system. For this large amount of data to be evaluated, it is necessary that an automatic classification method be used so that only signals with the desired characteristics are used to determine the parameters of interest. This aspect is highlighted in several publications which present new methods for classification and characterization using digital signal processing and computational intelligence tools (Angrisani et al, 1998; Santoso et al, 2000a; Santoso et al, 2000b and Huang et al, 2002; Machado et al, 2009; Rodriguez et al, 2010 ).

The first use of wavelet transform in power systems is credited to (Ribeiro, 1994). In recent years, wavelet transform - WT, a powerful tool for digital signal processing, has been proposed as a new technique for monitoring and analysis of different disturbances types in power systems (Machado et al, 2009; Mokryani, 2010; A. Rodriguez et al, 2010; Gong Jing, 2010, 2011). Wavelets, along with computational intelligence techniques like artificial neural networks and fuzzy logic, have been used successfully in automatic classification of power

The present work aims to develop an automated system for classifying power quality problems with respect to the fault type that has occurred and the electric phase involved, and quantify SDVV in electrical power systems from the available oscillography in the electrical utilities post-operation centers, to form a parameter database characterizing power quality problems. The proposed methodology uses the wavelet transform to obtain a characteristic pattern to represent the phenomenon and a probabilistic neural network for

Wavelets are functions that satisfy certain mathematical requirements. The wavelet name comes from the fact that they must be oscillatory (a wave), and be well placed, therefore exhibiting short time duration. There are several wavelet types, usually grouped into

Wavelets are used to represent data or other functions in a similar way as the Fourier analysis uses sines and cosines. The signal analysis by wavelet transform has advantages over traditional methods using Fourier analysis when the signals have time discontinuities

quality problems. (Machado et al, 2009; Mokryani, 2010; Rodriguez et al, 2010)

families, from which the Daubechies is one of the best known.

or present a non-stationary oscillatory behavior.

certain time intervals, for example, months or years.

classification.

**2. Wavelet transform** 

The wavelet transform is a technique similar to the windowed Fourier transform with the difference that the window width is variable. The wavelet analysis allows the use of large time intervals when it is desired to get low frequency information and shorter time intervals when the interest is to obtain high frequency information. Unlike Fourier analysis that uses sines and cosines, wavelet analysis uses wavelets. Figure 1 shows as an example, the Daubechies wavelet, db8.

Wavelets sets are employed to approximate signals, and each set consists of scaled versions (compressed or expanded) and translated (time shifted) from a single wavelet, called mother wavelet.
