**6. References**

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

According to the definition in (IEEE Std. PC37.114, 2004), error percentage of fault location

Some results obtained from the proposed DWT-NN technique are shown in Table 2. As seen in results, the error values are reasonable values and satisfactory. According to 4.2.1, the time of the fault detection and location is 4.6 *ms* equal to 46 samples per 10 *kHz* sampling rate. Therefore, this technique can be well used to estimate the fault detection and location

Real segment number Calculated value Error value Error %

Table 2. The results of fault location under db4 mother wavelet and 5 decomposition levels

Wavelet transform is a powerful signal processing tool used in power systems analysis. The most of applications of wavelet analysis in power systems include analysis and study of power quality, partial discharges, forecasting, measurement, protection and transients. It transforms a time-domain waveform into time-frequency domain and estimates the signal in

The most popular applications of WT are related to CWT, DWT and WPT techniques. CWT generates a huge amount of data in the form of wavelet coefficients with respect to change in scale and position. This leads to large computational burden. To overcome this limitation,

According to the done research, DWT is also extensively used to analyze the most of phenomena of power systems. However, an extensive study should be carried on applying DWT for power and RMS measurements. Because in MRA implemented by DWT filter banks, a signal is decomposed into non-uniform frequency sub-bands. However, for harmonic identification purposes, it is more useful if the signal is decomposed into uniform

DWT is used, as do in digital computers by applying DWT on discretized samples.

frequency sub-bands. This can be achieved using WPT filter banks.

4 3.8086 -0.1914 -0.96 14 4.0467 0.0467 0.23 29 29.0903 0.0903 0.45 37 37.1833 0.1833 0.92 51 51.1034 0.1034 0.52 66 65.7872 -0.2128 -1.06 74 74.0679 0.0679 0.34 86 86.1994 0.1994 1.00 95 94.8874 -0.1126 -0.56 103 103.2897 0.2897 1.45 112 111.7134 -0.2866 -1.43

*lengthline*

*valueerror error* % (15)

estimation is determined as follows:

in a specific transmission system.

**5. Conclusion** 

the time and frequency domains simultaneously.


Application of Wavelet Analysis in Power Systems 243

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**12** 

*México* 

**Discrete Wavelet Transform Application** 

José Antonio Gutiérrez-Gnecchi and Francisco Rivas-Dávalos

**Faults in FACTS Environment** 

*Instituto Tecnológico de Morelia, Morelia, Michoacán,* 

Enrique Reyes-Archundia, Edgar L. Moreno-Goytia,

**to the Protection of Electrical Power System:** 

**A Solution Approach for Detecting and Locating** 

The Wavelet Transform has been widely used to process signals in engineering and sciences areas. This acceptance is rooted on its proven capability to analyze fast transients signals which is difficult to perform with the FFT. In the area of electrical engineering, a number of publications have been presented about the analysis of phenomena in electrical grid at medium and high voltage levels. Some solutions have focused on the power quality (Chia-Hung&Chia-Hao, 2006; Tse, 2006), short-term load forecasting (Chen, 2010) and protection of power systems (Kashyap&Shenoy, 2003; Ning&Gao, 2009). However, there are few contributions in the open literature focusing in using WT for implementing relaying protection algorithms in power grids with presence of FACTS. The Thyristor Controlled Series Capacitor (TCSC), the Universal Power Flow Controller (UPFC), the Static Synchronous Series Compensator (SSSC), and the Statcom are some of the power controllers developed under the umbrella name of "Flexible AC Transmission Systems" (FACTS). These devices play a key role in nowadays electrical networks because they have the capability of improving the operation and control of power networks (power transfer, transient stability among others characteristics). Collateral to their many strong points, the FACTS controllers also have secondary effects on the grid that should be taken into account

In power grids, -transmission lines included-, there are three-phase, two-phase and singlephase fault events. At fault occurrence of any type, a fast transient signal, named travelling wave-, is produced and propagates through the power lines. The travelling waves are helpful in determining the fault location in such line, faster than using other methods, if the

This chapter presents the application of the Discrete Wavelet Transform (DWT) for extracting information from the travelling waves in transmission line and separate such waves from the signals associated to the TCSC and SSSC. This signal discrimination is

for engineering the next generation of protection schemes.

appropriate tools are used.

useful to improve protections algorithms.

**1. Introduction** 

