Multiwavelet Theory And Its Application Study In Power System Fault Signals Processing

Multiwavelet theory is new wavelet construction theory based on traditional wavelet theory. Multiwavelet can own symmetry, orthogonality, short support and high order vanish moments, however traditional wavelet cannot possess all these properties at the same time. The research and applications on multiwavelet theory are at beginning, and its' application in power system is not reported now. In this paper, based on the study of multiwavelet theory, the problems on applications are proposed and discussed, the corresponding solutions are put forward and multiwavelet theory is extended. This theory is first introduced into the fault signal processing in power system, and new application algorithms are proposed. The aim of this paper is to extend the theory and application of multiwavelet and introduce novel methods for fault signal processing, which may have a considerable impact on engineering application.From the key problem - pre-processing of multiwavelet applications, the necessity of pre-processing method is discussed. After the influence of pre-processing methods to multiwavelet filters response are analyzed and studied in detail, the two estimation standards are proposed to choose the best pre-processing method. In addition, the simplified algorithm of multiwavelet decomposition and reconstruction, the boundary problem of multiwavelet transformation, the reconstruction effect comparison between traditional wavelet and multiwavelet, "Gibbs" phenomena in multiwavelet transformation are studied and discussed.In this paper, multiwavelet theory is extended including multiwavelet construction with lifting scheme and combination of multiwavelet and neural network. Through presentation and discussion of traditional wavelet construction with lifting scheme, the multiwavelet construction with lifting scheme is introduced. The extension of Vetterli-Herley theorem under multiwavelet condition is overall proved in detail. Based on equivalent scalar filters banks, a kind of multiwavelet construction with lifting scheme and corresponding theorem are proposed. The function approximation abilities of wavelet transformation and neural network are analyzed and their relations are deeply studied. The corresponding wavelet functions are constructed with different aviation functions of neural networks. The applications in fault signal classification and data compression of power system are studied and simulated. Through the introduction of multiwavelet network, other two kinds of multiwavelet networks are proposed. Thetheorems for function approximation abilities of some wavelet networks and multiwavelet networks are proposed and proved.The multiwavelet analysis is first introduced into fault signal processing in power system, including time-frequency analysis, signal de-noising and data compression for transmission lines fault transient signal. Through a great deal of simulation test, it is shown that the applications are successful and outperform the traditional wavelet analysis as a whole. In addition, the choice of best multiwavelet packet base is discussed and computed. Considering the shortage of common de-noising algorithm of multiwavelets, a kind of new algorithm is proposed and applied, which is based on adaptive shrinkage value. In the end, a kind of new multiwavelet data compression plan based on best pre-processing method is proposed, and corresponding validity and feasibility are validated through simulations.