**5. Results**

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

three decoupled modes: mode 0 (zero), mode α and mode β, so the three phases are decomposed into nine modes, three for each phase. As mode 0 is the same for all phases, this mode can be calculated only once, reducing to seven the number of signals. Therefore, the three phase voltage signals are decomposed by the multiresolution analysis and the firstlevel detail 3-dimensioned array is used with the modal matrix to decoupling the original

Where ��� ��� are the voltage wavelet coefficients corresponding to the coupled and decoupled phases respectively and *W* is the decoupling matrix. It is noteworthy that only the voltage signals can be decoupled by the method presented here and the operation described in Eq. (14) should be performed on each signal sample. The matrix *W* is described

 

This way it is obtained a system that provides seven outputs, being mode α and mode β for each phase and a mode 0 which is common to the three phases. These modes contain the wavelet transform coefficients of the three-phase decoupled input signals. The linearity properties of the wavelet and modal transformations ensure that they can be carried out in a cascading way without causing problems to the classifier algorithm results. So, it is obtained a classification pattern that is represented by a matrix with seven

The ANN used for the SDVV classification, named PNN1, is composed of three classes,

Class 1 – Voltage sags and interruptions, which are characterized by voltage

Class 2 - Adequate voltage, which is characterized by magnitudes between 0.9 p.u. and

Class 3 – Voltage swell, which is characterized by magnitudes between 1.1 p.u. and 1.8

The training values of each class were obtained from points on the curve given in Figure 9, resulting in 19 values stored in the PNN1. As each class covers a different magnitude range, it was established 9 values for class 1, 3 values for Class 2 and 7 values for Class 3. The weight matrix of the competitive layer is a 3x19 matrix, which corresponds to the 19 training values and the three classes considered. The input pattern to be classified consists of a three elements vector, each representing the characteristic of each phase voltage; and the PNN1 output consists of a three elements vector, each one indicating the classification

1 −√3 −1 2 0 −1 −1 √3 2

 √3 −√3 0 � �

��� � ���� (14)

(15)

Mathematically the modal transformation consists of a matrix operation as follows:

12 0 1 −1 √3 1 −1 −√3

signals.

by (Silveira; et al, 1999):

columns and 192 rows.

namely:

1.1 p.u.;

corresponding to each phase.

p.u.

**4.2 Artificial neural networks structures** 

magnitudes smaller than 0.9 p.u.

� � � ��

> In order to evaluate the performance of the proposed method in classifying SDVV, 311 voltage oscillographic signals obtained from a real power system were used. The oscillographic signals were numbered from 1 to 311 for the purpose of identification. The electrical power system is a 500 kV/230 kV transmission system connecting Tucuruí Hydroelectric Power Plant located in the south of the State of Pará-Brazil, to load centers in the northern region, which is operated by Eletronorte, a generation and transmission utility in the north of Brazil. The oscillography files used are from the 230 kV substation Guamá, located in Belém city, the capital of the state of Pará, and corresponds to a time period within 2004/2005.

> Table 2 shows the results corresponding to the PNN1 output. The SDVV parameters represented in Table 2 are the time duration in cycles, and magnitude in p.u. As can be seen, 24 voltage signals were classified as having SDVV.

Application of Wavelet Transform and Artificial Neural Network to

error in this case, as presented by the 100% result in Table 3.

Two-Phase and Two-

Three-Phase and Three-

Table 3. Results for fault type classification

discharges.

**6. Conclusion** 

analysis procedures are needed.

Fault Type Simulated

Single-Phase to Ground 1,029 94%

Phase to Ground 2,058 94,6

Phase to Ground 686 100%

With the purpose of testing the performance of the proposed method in classifying real oscillographic signals, some Eletronorte operational reports in the period 2007/2008 were analyzed which contained 31 labeled transient occurrences, being 17 due to short circuits, and 14 due to lightning discharge. For considering lightning discharges (LD) a new class was added to PNN2, and 7 of the 14 signals were selected for training the PNN2 and the remaining signals were used for testing. The testing signals were applied to the trained PNN2 achieving 100% accuracy for short circuits and 85,7% for lightning

This work presented a methodology for automatic SDVV classification as well as fault type identification using digital signal processing and computational intelligence techniques. Real power system data were used and satisfactory results for both SDVV and fault type classification were obtained. The implementation of the proposed methodology as part of a computational tool and its integration with the post-operational utility analysis routines will enable the automatic analysis of a larger number of signals waveforms, allowing the methodology proposed here to serve as a basis for future applications where automatic

One should also note that the wavelet used in this work was chosen due to its good performance in determining the disturbance location in the signal waveform. Various wavelets orders from db2 to db16 were tested and the db4 wavelet presented the best performance, and considering also the fact that it has filters with few coefficients, the processing time for the signals decomposition is greatly reduced, which is an important

characteristic when a large number of signals are to be analyzed.

Extract Power Quality Information from Voltage Oscillographic Signals in Electric Power Systems 193

The simulation studies included 1,029 single-phase to ground short-circuit; 2,058 two-phase and two-phase to ground short-circuits; and 686 three-phase and three-phase to ground short circuits. For the PNN2 training, seven case studies for each fault type as listed in Table 1 were used as input patterns, and the remaining cases were used for testing. Table 3 shows the classification results, noting that misclassification occurred for single-phase and twophase to ground short circuits, with 6% and 5.4% respectively. Also 58% of the three-phase short circuit were classified as three-phase to ground short circuits, but considering that these two fault types can be considered as a single class there would be no classification

Cases

Results (Correct Classification)

According to data in Table 2 it may be seen that the PNN1 classification is consistent with the magnitude values calculated for the SDVV. It is observed that in most cases voltage sags were detected in all three phases (classification 1.1.1), and for signals 267 and 268 voltage sags were detected only in phase C, while phase A, and B exhibited adequate voltage magnitudes (classification 2.2.1). It is also worth noting that all these results were compared with the real original voltage waveforms, which proved the results correctness as obtained by the wavelet multiresolution analysis and by the PNN1 classification mechanism.



For the fault type classification and the faulted phase identification the same 230 kV/500 kV electrical power system was used in which short-circuits were simulated along the transmission lines by varying the incidence angle, and the short-circuit resistance to obtaining a set of voltage waveforms corresponding to the different simulated fault types, using the simulation software ATP.

The simulation studies included 1,029 single-phase to ground short-circuit; 2,058 two-phase and two-phase to ground short-circuits; and 686 three-phase and three-phase to ground short circuits. For the PNN2 training, seven case studies for each fault type as listed in Table 1 were used as input patterns, and the remaining cases were used for testing. Table 3 shows the classification results, noting that misclassification occurred for single-phase and twophase to ground short circuits, with 6% and 5.4% respectively. Also 58% of the three-phase short circuit were classified as three-phase to ground short circuits, but considering that these two fault types can be considered as a single class there would be no classification error in this case, as presented by the 100% result in Table 3.


Table 3. Results for fault type classification

With the purpose of testing the performance of the proposed method in classifying real oscillographic signals, some Eletronorte operational reports in the period 2007/2008 were analyzed which contained 31 labeled transient occurrences, being 17 due to short circuits, and 14 due to lightning discharge. For considering lightning discharges (LD) a new class was added to PNN2, and 7 of the 14 signals were selected for training the PNN2 and the remaining signals were used for testing. The testing signals were applied to the trained PNN2 achieving 100% accuracy for short circuits and 85,7% for lightning discharges.
