volume | PIER Journals

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 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 Multivectorial Euclidean Vector Space structure (CG_n-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 clarification 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.

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Dr. Manuel Castilla

Dr. Juan Carlos Bravo

Dr. Manuel Ordonez

Dr. Juan Carlos Montano