Analysis of electrical transients in power systems via a novel wavelet recursion method

This work utilizes wavelet analysis a relatively new mathematical tool, to develop a new method of analysis for electrical transients in electric power systems. Techniques which are currently employed fall into two main categories: time domain or the integral transform domain. Time domain methods include the mathematical solution of differential equations and companion circuit techniques. The integral transform domain methods include Laplace transform and frequency (e.g., Fourier transform) analysis. Both of the aforementioned categories can be stressed when solving systems of equations with a wide eigenspectrum or when system of equations is subjected to a nonstationary forcing function. One of the benefits of wavelet analysis, however, is the ability to easily resolve signals of a nonstationary nature. In this thesis, four wavelet recursion formulae--the Right Formula Backward Difference (RFBD), the Left Formula Backward Difference (LFBD), the Right Formula Forward Difference (RFFD), and the Left Formula Forward Difference (LFFD)--are derived for the solution of the differential equations that are germane to the analysis of electric power systems. The convergence properties of the formulae are discussed and several examples are presented. It is shown by these examples, that the method developed in this work is a viable and sometimes preferred alternative to the current methods of electrical transient analysis of power systems