4. Wavelets transform application in electric power system

Refs. [1, 13, 14] conducted studies related to this chapter. These authors also present a literature review on the application of WT in power electrical systems.

By means of the bibliographic review, it is possible to highlight certain topics of interest for researchers:

• Power quality

The procedure starts with passing this signal x[n] through a half band digital low-pass filter with impulse response h[n]. Filtering a signal corresponds to the mathematical operation of convolution of the signal with the impulse response of the filter. The convolution operation in discrete time is defined as follows [2]:

> ∞ k¼�∞

A half band low-pass filter removes all frequencies that are above half of the highest frequency in the signal. For example, if a signal has a maximum of 1000 Hz component, then half band low-pass filtering removes all the frequencies above 500 Hz. However, it should always be remembered that the unit of frequency for

After passing the signal through a half band low-pass filter, half of the samples can be eliminated according to the Nyquist's rule. Simply discarding every other sample will subsample the signal by two, and the signal will then have half the number of points. The scale of the signal is now doubled. Note that the low-pass filtering removes the high frequency information but leaves the scale unchanged. Only the sub-sampling process changes the scale. Resolution, on the other hand, is related to the amount of information in the signal, and therefore, it is affected by the filtering operations. Half band low-pass filtering removes half of the frequencies, which can be interpreted as losing half of the information. Therefore, the resolution is halved after the filtering operation. Note, however, the sub-sampling operation after filtering does not affect the resolution, since removing half of the spectral components from the signal makes half the number of samples redundant anyway. Half of the samples can be discarded without any loss of information.

x k½ �� h n½ � � k (9)

h k½ �� x n½ � � k (10)

x n½ �� g½ � 2k � n (11)

x n½ �� h½ � 2k � n (12)

x n½ � ∗ h n½ �¼ ∑

This procedure can mathematically be expressed as [2]:

mathematically be expressed as follows [2]:

respectively, after sub-sampling by 2.

3. Wavelets theory advantage

82

y n½ �¼ ∑

yhigh½ �¼ k ∑

ylow½ �¼ k ∑

is presented. One of the main advantages of wavelets is that they offer a

n

n

where yhigh[k] and ylow[k] are the outputs of the high-pass and low-pass filters,

In [12], an application of WT and its advantages compared to Fourier transform

∞ k¼�∞

The decomposition of the signal into different frequency bands is simply obtained by successive high-pass and low-pass filtering of the time domain signal. The original signal x[n] is first passed through a half band high-pass filter g[n] and a low-pass filter h[n]. After the filtering, half of the samples can be eliminated according to the Nyquist's rule, since the signal now has a highest frequency of p/2 radians instead of p. The signal can therefore be sub-sampled by 2, simply by discarding every other sample. This constitutes one level of decomposition and can

discrete time signals is radians.

Wavelet Transform and Complexity


Figure 3 shows the percentage of publications in each area. The areas in which more works have been developed are the power quality and protection field. The next section presents a general description of wavelet application in the selected areas of power systems. There are more works in these areas; however, no details will be entered due to space issues and that the approach to the topic used WT is similar.

### 4.1 Partial discharges

Partial discharges are difficult to detect because of their short duration, high frequency, and low amplitude. However, the use of WT can not only detect them

Finally, the characteristic impedance of a transformer can be obtained through its transient response [26]. With this, we can easily make a verification of the state

In the search for shorter downtimes and the maximization of the life time of the energy system equipment, it repeats itself to increasingly finer methods for analysis. In the recent years, we have begun to analyze the protections of voltage transformers (TT) and current transformers (CT) by WT [27]. This was done previously in the use of the Fourier Transform (FFT) and the current protections of the internal fault current. Refs. [28–31] study the differentiation of these currents by theoretical methods. This means that the test in the field is not done but the results of the simulations give positive results, an exception of [31] where the methods are applied to a test TT. For the development of differential protections, [30, 32–34] analyze the transients and extract the predominant signal from the internal fault; the method has been tested with different faults and an efficient algorithm for online analysis has been obtained. In [33–41], WT is used for fault diagnostic and

There has been a great effort in different works to evaluate the different mother wavelet. Thus, [33, 34] present a comprehensive analysis involving an important number of wavelets to prove the efficiency in power transformer protection.

Another important part is between disruptive currents and fault currents in the

With the increase of the use of electronic equipment, it has become a necessity to study the quality of energy. The loads, having a stationary or non-stationary state, are no longer easily analyzed, so we resort to mathematical tools capable of classifying and characterizing these states. In this network, transient disturbance occurring in the network can be classified as voltage drops, voltage increases,

The main topics of study are the harmonics; these are present in the waves and

A practical application of the CWT is the real-time monitoring of voltage and current signals for the rapid detection and elimination of transient events that may worsen the quality of the electric service. Previously, the first subject of study in terms of energy quality was established, but this is only a small part of the faults found in the energy system. Faults must be identified in order to perform an

are common to see in the electrical networks, and so the first step would be to identify them and isolate their behavior in order to eliminate these disturbances. Ref. [49–51], using WPT, perform a method in which the fundamental harmonic and higher order harmonics can be extracted, which is a method applicable to energy networks for monitoring them. For the same application [52], they have formulated using CWT, an algorithm used to identify the variations of frequency,

The bus zone protection scheme is considered for the detection of transient current in [44]. In the electric machine area, [45] proposed the use of the WT for fault diagnostic using current signal. The transmission line fault detection with WT in the presence of wind power generation is studied in [46, 47] approach, a study on fault detection in compensated transmission line (TCSC technology). In [48],

earth, where the results were analyzed with computer programs [42, 43].

wavelet analysis is used for fault detection in hybrid energy source.

momentary interruptions, harmonics, and transients, among others.

efficient analysis and be able to act on them as soon as they occur.

harmonics, sub harmonics, and inter harmonics.

of the transformer using the WT coefficients.

DOI: http://dx.doi.org/10.5772/intechopen.85274

Wavelet Transform Analysis to Applications in Electric Power Systems

transient event identification in transformer operation.

4.3 Power system protection

4.4 Power quality

85

Figure 3. Wavelet publication percentage in different power system areas.

but also isolate them by frequency bands for their study, performing a multiresolution analysis. An important study is the filtering of noise in PD signals. In this sense, [15, 16] propose the recognition and categorization of PDs, for the study of transformer failures.

In [15], an adaptive filter is used to obtain PD without noise or interference for online studies. In [16], it is posed by means of a sophisticated equipment to obtain the currents and through WT to filter the PD and to be able to carry out its later study. If we follow the line of online monitoring, it can be seen in [17] that using a high-frequency transducer, the PD can be extracted to obtain analysis in transformers in service. We talked about how to get them and how to remove the noise in the signals, we just need to locate them. Ref. [18] proposes a PD injection method in preestablished nodes to obtain the plant model to measure at separate points.
