Teorias sobre fasores dinâmicos obtidas a partir de transformadas integrais

Abstract

The Classical Phasor Theory goes back to the pioneer work of Charles Proteus Steinmetz in the study of alternating current electrical circuits. According to Steinmetz, a classical or static phasor is a complex number that represents a sinusoidal function whose amplitude, phase and angular frequency are constants and it transforms ordinary differential equations with constant coefficients, which are models for alternating current electrical circuits, in linear systems with complex coefficients. When either amplitude, phase or angular frequency is no longer constant, the phasor theory must be adapted in such a way to preserve the classical results. In this new theory, which deals with a large class of functions rather than only sinusoidal functions, the phasor is called dynamic or timevariable phasor. Following this line, the main objective of this work is to present three new theories about dynamic phasors built from integral transforms, namely, the short-term Fourier transform, the generalized Laplace transform and the Hilbert transform. More precisely, the dynamic phasors arise through injective linear operators between suitable vector spaces and they have similar properties to those of the dynamic phasors usually found in the literature.