Geometric Power and Poynting Vector: a Physical Derivation for Harmonic Power Flow using Geometric Algebra

This document aims to establish an alternative physical formulation for the harmonic power flow in electrical systems provided by Geometric Algebra (GA) and the Poynting Vector (PV) and Poynting Theorem (PT). Given the traditional definition of PV (Abraham approach) as the vector product of the electric field and magnetic field, we exploit the property of the vector product as a dual form of the much more powerful wedge product operator from exterior algebra. Using concepts of vector spaces, we develop a completely GA-based approach founded on top of the isomorphism among periodic time-domain signals and Euclidean spaces. Our investigations shed more light on the long-running discussion of electric power flow in non-sinusoidal and non-linear electrical power systems.