**4.1.1.2 Transients characterization parameters**

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 classification task.

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 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 signals.

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

$$d\_{\nu0} = \mathcal{W}d\_{\nu1} \tag{14}$$

Application of Wavelet Transform and Artificial Neural Network to

types as listed in Table 1.

corresponding to the training vectors.

Single-Phase Short Circuits

Short Circuits

**5. Results** 

within 2004/2005.

Two-Phase and Two-Phase to Ground

Three-Phase and Three-Phase to Ground

24 voltage signals were classified as having SDVV.

Table 1. Short Circuits Types

Extract Power Quality Information from Voltage Oscillographic Signals in Electric Power Systems 191

For transient analysis 11 classes were considered, which correspond to the short circuit

The PNN2 training matrix has stored seven classification patterns for each class, related to bus voltages. As each pattern has seven vectors derived from the modal transformation, each class is composed of 49 vectors with 192 rows by 49 columns. The output matrix consists of 11 rows, corresponding to the disturbances types classes, and 539 columns

Short Circuits Phases ABC;Phases ABC-to Ground

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

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,

Phase A to Ground

Phase B to Ground

Phase C to Ground

Phases AB; Phases AB-to Ground

Phases AC; Phases AC-to Ground

Phases BC; Phases BC-to Ground

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 by (Silveira; et al, 1999):

$$W = \frac{1}{3} \begin{pmatrix} 1 & 2 & 0 & 1 & -\sqrt{3} & -1 & \sqrt{3} \\ 1 & -1 & \sqrt{3} & 2 & 0 & -1 & -\sqrt{3} \\ 1 & -1 & -\sqrt{3} & -1 & \sqrt{3} & 2 & 0 \end{pmatrix}^t \tag{15}$$

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 columns and 192 rows.

#### **4.2 Artificial neural networks structures**

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


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 corresponding to each phase.

For transient analysis 11 classes were considered, which correspond to the short circuit types as listed in Table 1.

The PNN2 training matrix has stored seven classification patterns for each class, related to bus voltages. As each pattern has seven vectors derived from the modal transformation, each class is composed of 49 vectors with 192 rows by 49 columns. The output matrix consists of 11 rows, corresponding to the disturbances types classes, and 539 columns corresponding to the training vectors.


Table 1. Short Circuits Types
