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2009-06-23
An Approach to the Multivectorial Apparent Power in Terms of a Generalized Poynting Multivector
By
Manuel Castilla,

    Dr. Manuel Castilla

    Electrical Engineering Department

    University of Sevilla

    Spain

    Homepage

Juan Carlos Bravo,

    Dr. Juan Carlos Bravo

    Electrical Engineering Department

    University of Sevilla

    Spain

    Homepage

Manuel Ordonez,

    Dr. Manuel Ordonez

    Applied Mathematics Department

    University of Sevilla

    Spain

    Homepage

Juan Carlos Montano

    Dr. Juan Carlos Montano

    Spanish Research Council (CSIC)

    Spain

    Homepage

Progress In Electromagnetics Research B, Vol. 15, 401-422, 2009
doi:10.2528/PIERB09042402 | Google Scholar

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 (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 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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Citation
Manuel Castilla, Juan Carlos Bravo, Manuel Ordonez, and Juan Carlos Montano, "An Approach to the Multivectorial Apparent Power in Terms of a Generalized Poynting Multivector," Progress In Electromagnetics Research B, Vol. 15, 401-422, 2009.
doi:10.2528/PIERB09042402
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