Recent Applications of Wavelet Theory

**Chapter 14**

**Abstract**

signal denoising

**1. Introduction**

300 MHz to 1 GHz.

**311**

exponentially damped shape [2].

Measurements

A Wavelet Threshold Function for

Based on the wavelet transform filtering theory, the chapter will describe the elaboration of a wavelet threshold function intended for the denoising of the partial discharge phenomenon measurements. This new function, conveniently named Fleming threshold, is based on the logistic function, which is well known for its utility in several important areas. In the development is shown some variations in the application of the Fleming function, in an attempt to identify the decomposition levels where the thresholding process must be more stringent and those where it can be more lenient, which increases its effectiveness in the removal of noisy coefficients. The proposed function and its variants demonstrate excellent results

compared to other wavelet thresholding methods already described in the

The analysis of the Partial Discharges (PD) phenomenon, which manifests itself in the existing imperfections into the insulation of high voltage equipment have received global acceptance as an important tool for the predictive diagnosis of the operational conditions of these, allowing taking measures that can safeguard both

PD are short duration impulsive signals and, consequently, these can be detected

in a wide frequency range, from a few kHz to GHz. Normally, there is a direct relationship between the frequency range where there is a higher incidence of PD pulses and the type of high-voltage equipment evaluated, e.g. transformers and generators usually emit pulses from a few tens of kHz up to about 30 MHz [1], whereas Gas Insulated Substations (GIS) are affected by very fast pulses ranging from 300 MHz to 3 GHz and for cables the spectrum covers frequencies from

**Figure 1** shows two examples of measured PD pulses in two different HV equipment, a GIS and a hydro generator. Note the marked white noise presence. The pulses normally have an exponentially damped oscillatory shape or only an

**Keywords:** wavelet transform, threshold function, partial discharge,

the material and the power supply quality of the electrical system.

literature, including the famous Hard and Soft functions.

Treatment of Partial Discharge

*Caio F.F.C. Cunha, Mariane R. Petraglia,*

*André T. Carvalho and Antonio C.S. Lima*

#### **Chapter 14**
