**4.1.1 Input patterns**

Power systems electromagnetic phenomena are characterized by categories according to their spectral content, magnitude and duration (IEEE Std 1250, 1995). These phenomena classification into categories requires an analysis methodology that very frequently must be individualized, which prevents this procedure applicability when the number of signals to be evaluated is very large. Then, procedures to extract signals relevant characteristics have been proposed, so that they can be automatically classified into a specific category. Obtaining parameters for characterizing a given signal usually requires a transformation from the time domain to another domain where the specific characteristics are highlighted.

The use of wavelet transform has proved adequate for obtaining electrical signals characteristics which can be used in classification processes. Studies such those presented in (Lee et al, 1997; Chan et al, 2000; Santoso et al, 2000c; Ramaswamy et al, 2003; Zwe-Lee et al, 2003; Zwe-Lee, 2004 & Machado et al, 2009), use characteristic vectors based on the multiresolution analysis decomposition levels coefficients as input to computational intelligence-based systems to classify different power quality events. The characteristic vectors magnitudes depend on the number of decomposition levels used for the analysis, or the number of coefficients of a given decomposition level. The method proposed here uses the Daubechies wavelet, db4, and the voltage signals are decomposed into three levels. The first signal detail level is used to determine the time instant the disturbance has started and also to characterize the transients in the fault type identification, while the third signal approximation is used to characterize SDVV. The computational algorithms were implemented on MATLAB, and also coded in Java.

Figure 7(a) shows an original voltage waveform in p.u. obtained from a digital disturbance register (DDR) presenting a voltage sag. The original waveform is decomposed into three resolution levels. In Figures 7(b-d) the signal details from level 1 to level 3 are presented and in Figure 7(e) the signal approximation at level 3. Details retain the high-frequency information contained in the signal, divided into frequency bands which are function of the sampling rate used in the acquisition process. In case of Figure 7, the sampling rate is 96 samples per cycle of 60 Hz, or 5,760 samples per second.

Fig. 7. Signal decomposition in 3 levels. In (a) original signal. From (b) to (d) details from level 1 to level 3, and (e) level 3 approximation.

The wavelet transform performance to detect disturbances in electrical signals is substantially improved if a procedure for reducing noise level is applied to the decomposition level coefficients to be used in the detection process. This feature is highlighted in (Yang et al, 1999; 2000 & 2001). So, to better characterize the disturbance location in the signal, it is applied the following algorithm presented in (Misiti et al, 2000), to the previously selected decomposition level:

$$
\hat{d}\_s(\mathbf{n}) = \begin{vmatrix} d\_s(\mathbf{n}) - \eta\_s & \text{if} & \begin{vmatrix} d\_s(\mathbf{n}) \end{vmatrix} \ge \eta\_s \quad \text{and} \quad d\_s(\mathbf{n}) > 0 \\ d\_s(\mathbf{n}) + \eta\_s & \text{if} & \begin{vmatrix} d\_s(\mathbf{n}) \end{vmatrix} \ge \eta\_s \quad \text{and} \quad d\_s(\mathbf{n}) < 0 \\ 0 & \text{if} & \begin{vmatrix} d\_s(\mathbf{n}) \end{vmatrix} < \eta\_s \end{vmatrix} \tag{12}
$$

Where:

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

encountered in the power system topology. In the case study presented here, the power transmission system presents 230 kV and 500 kV voltage levels. The standardization is performed by converting the phase voltages to per unit (p.u.) values considering the voltage

In the processing stage, the wavelet transform is applied to the voltage waveforms to obtaining signals patterns that characterize short duration voltage variations (SDVV) and transient variations (TV) due to system faults. These obtained patterns are used as inputs to two Probabilistic Neural Networks for SDVV classification (PNN1), as well as to classify the fault type that has occurred (PNN2). The classification results will form a database which

Power systems electromagnetic phenomena are characterized by categories according to their spectral content, magnitude and duration (IEEE Std 1250, 1995). These phenomena classification into categories requires an analysis methodology that very frequently must be individualized, which prevents this procedure applicability when the number of signals to be evaluated is very large. Then, procedures to extract signals relevant characteristics have been proposed, so that they can be automatically classified into a specific category. Obtaining parameters for characterizing a given signal usually requires a transformation from the time domain to another domain where the specific

The use of wavelet transform has proved adequate for obtaining electrical signals characteristics which can be used in classification processes. Studies such those presented in (Lee et al, 1997; Chan et al, 2000; Santoso et al, 2000c; Ramaswamy et al, 2003; Zwe-Lee et al, 2003; Zwe-Lee, 2004 & Machado et al, 2009), use characteristic vectors based on the multiresolution analysis decomposition levels coefficients as input to computational intelligence-based systems to classify different power quality events. The characteristic vectors magnitudes depend on the number of decomposition levels used for the analysis, or the number of coefficients of a given decomposition level. The method proposed here uses the Daubechies wavelet, db4, and the voltage signals are decomposed into three levels. The first signal detail level is used to determine the time instant the disturbance has started and also to characterize the transients in the fault type identification, while the third signal approximation is used to characterize SDVV. The computational algorithms were

Figure 7(a) shows an original voltage waveform in p.u. obtained from a digital disturbance register (DDR) presenting a voltage sag. The original waveform is decomposed into three resolution levels. In Figures 7(b-d) the signal details from level 1 to level 3 are presented and in Figure 7(e) the signal approximation at level 3. Details retain the high-frequency information contained in the signal, divided into frequency bands which are function of the sampling rate used in the acquisition process. In case of Figure 7, the sampling rate is 96

can be used to evaluate power quality indices for the electrical system.

peak value as base voltage.

**4.1 Processing stage** 

**4.1.1 Input patterns** 

characteristics are highlighted.

implemented on MATLAB, and also coded in Java.

samples per cycle of 60 Hz, or 5,760 samples per second.


The*<sup>s</sup>* value used was 10% of the maximum absolute value of the decomposition level coefficients considered, as proposed in (Santoso et al, 1997).

A voltage waveform containing voltage sag is shown in Figure 8(a). In (b) it is presented the details level used to detect the disturbance beginning and (c) presents new details values after the noise reduction algorithm is applied. In (c) it can be observed smaller coefficients magnitudes over the entire signal which improves the algorithm performance used to detect the disturbance.

Application of Wavelet Transform and Artificial Neural Network to

disturbance magnitude ranging from zero to 1.8 p.u.

Fig. 9. Signal norm variation as a function of the SDVV magnitude.

which is used as input to the PNN for classification purpose.

**4.1.1.2 Transients characterization parameters** 

classification task.

So, the SDVV classification pattern is obtained by calculating the signal norm for 10 cycles counting from point *<sup>i</sup> p* , which represents the disturbance starting point. This procedure is applied to the voltage waveforms in phases A-B-C resulting a vector with three elements

In the transient analysis case, a two cycles long window is selected from the disturbance starting point which, for real electrical systems, is a time interval within which most of the protective devices operate. This considered signal is then normalized based on the biggest magnitude coefficient, for creating a vector related to each fault type to be analyzed in the

In three-phase transmission lines, phases are mutually coupled and therefore the high frequency variations generated during a disturbance may also appear in non-faulted phases. Using a modal transformation allows the coupled three-phase system to be treated as a system with three independent single-phase circuits. Each phase values are transformed into

**4.1.1.1 SDVV characterization parameters** 

Extract Power Quality Information from Voltage Oscillographic Signals in Electric Power Systems 189

As the signal magnitude and duration change during the SDVV occurrence, the norm value (Euclidian distance) will also change if the disturbed signal is considered. So, by monitoring changes in the norm of the third-level signal approximation (the level containing the fundamental frequency) and considering the signal disturbed portion, it can be obtained a standard value characterizing these signal changes. Figure 9 shows the signal norm variation as function of the signal magnitude for the third-level signal approximation of the multiresolution analysis. In this analysis, a 10 cycles signal window was considered and the

Fig. 8. (a) Original voltage waveform with voltage sag, (b) second details level, and (c) second details level after noise reduction.

The disturbance beginning point is found based on the following algorithm presented in (Gaouda et al, 2002)

$$m(n) = \begin{cases} 0 & \quad [\hat{d}\_s(n)]^2 < \sigma \\ 1 & \quad [\hat{d}\_s(n)]^2 \ge \sigma \end{cases} \tag{13}$$

where:

 is the standard deviation of <sup>ˆ</sup> <sup>2</sup> [ ( )] *<sup>s</sup> d n*

The algorithm (13) was originally proposed to find the disturbance start and end points. In this particular case, the interest is just the starting point, *<sup>i</sup> p* , which shall be considered as a reference for obtaining the phenomena pattern characterization in the classification stage. For this purpose the following algorithm is proposed:


If <sup>ˆ</sup> <sup>2</sup> [ ( )] *<sup>s</sup> d n* , return to step 4; If <sup>ˆ</sup> <sup>2</sup> [ ( )] *<sup>s</sup> d n* , *<sup>i</sup> p n* ;

6. End

Once the disturbance starting point is obtained, the next step is to determine the signal parameters to input the PNN in order to characterize SDVV and transients.

## **4.1.1.1 SDVV characterization parameters**

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

Fig. 8. (a) Original voltage waveform with voltage sag, (b) second details level, and (c)

The disturbance beginning point is found based on the following algorithm presented in

 

The algorithm (13) was originally proposed to find the disturbance start and end points. In this particular case, the interest is just the starting point, *<sup>i</sup> p* , which shall be considered as a reference for obtaining the phenomena pattern characterization in the classification stage.

Once the disturbance starting point is obtained, the next step is to determine the signal

:

parameters to input the PNN in order to characterize SDVV and transients.

<sup>ˆ</sup> 0 [ ( )] ( ) <sup>ˆ</sup> 1 [ ( )]

*m n*

2 2

(13)

*s s*

*d n*

*d n*

second details level after noise reduction.

is the standard deviation of <sup>ˆ</sup> <sup>2</sup> [ ( )] *<sup>s</sup> d n*

For this purpose the following algorithm is proposed:

, return to step 4;

(Gaouda et al, 2002)

1. Calculate <sup>ˆ</sup> <sup>2</sup> [ ( )] *<sup>s</sup> d n* ;

;

If <sup>ˆ</sup> <sup>2</sup> [ ( )] *<sup>s</sup> d n*

If <sup>ˆ</sup> <sup>2</sup> [ ( )] *<sup>s</sup> d n*

5. Compare the value of <sup>ˆ</sup> <sup>2</sup> ( ) *<sup>s</sup> d n* with

, *<sup>i</sup> p n* ;

2. Calculate

6. End

3. Make *n* 0 ; 4. Make *n n* 1 ;

where:

As the signal magnitude and duration change during the SDVV occurrence, the norm value (Euclidian distance) will also change if the disturbed signal is considered. So, by monitoring changes in the norm of the third-level signal approximation (the level containing the fundamental frequency) and considering the signal disturbed portion, it can be obtained a standard value characterizing these signal changes. Figure 9 shows the signal norm variation as function of the signal magnitude for the third-level signal approximation of the multiresolution analysis. In this analysis, a 10 cycles signal window was considered and the disturbance magnitude ranging from zero to 1.8 p.u.

Fig. 9. Signal norm variation as a function of the SDVV magnitude.

So, the SDVV classification pattern is obtained by calculating the signal norm for 10 cycles counting from point *<sup>i</sup> p* , which represents the disturbance starting point. This procedure is applied to the voltage waveforms in phases A-B-C resulting a vector with three elements which is used as input to the PNN for classification purpose.
