A Geometric Procedure for Computing Differential Characteristics of Multi-phase Electrical Signals using Geometric Algebra

Abstract

This paper presents exploratory investigations on the concept of generalized geometrical frequency in electrical systems with an arbitrary number of phases by using Geometric Algebra and Differential Geometry. By using the concept of Darboux bivector it is possible to find a bivector that encodes the invariant geometrical properties of a spatial curve named electrical curve. It is shown how the traditional concept of instantaneous frequency in power networks can be intimately linked to the Darboux bivector. Several examples are used to illustrate the findings of this work.