An Approach to the Multivectorial Apparent Power in Terms of a Generalized Poynting Multivector

Abstract

The purpose of this paper is to explain an exact derivation of apparent power in n-sinusoidal operation founded on electromagnetic theory, until now unexplained by simple mathematical models. The aim is to explore a new tool for a rigorous mathematical and physical analysis of the power equation from the Poynting Vector (PV) concept. A powerful mathematical structure is necessary and Geometric Algebra offers such a characteristic. In this sense, PV has been reformulated from a new Multivectorial Euclidean Vector Space structure (CGn-R3) to obtain a Generalized Poynting Multivector ( ~ S). Consequently, from ~ S, a suitable multivectorial form ( ~ P and ~D) of the Poynting Vector corresponds to each component of apparent power. In particular, this framework is essential for the clari¯cation of the connection between a Complementary Poynting Multivector (~D) and the power contribution due to cross-frequency products. A simple application example is presented as an illustration of the proposed power multivector analysis.