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\begin{document}

\title{Geometric Foundations of Power Theory for Multiphase AC Systems in the
Frequency Domain}



\author[1,1]{Francisco G. Montoya }%
\author[2]{Jorge Ventura }%
\author[2]{Francisco
M. Arrabal-Campos }%
\author[2]{alfredo alcayde }%
\affil[1]{university of almeria}%
\affil[2]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
This research paper presents a new approach to power definitions in
multiphase AC systems in the frequency domain from a purely geometric
approach. The theoretical foundation is based on Geometric Algebra (GA)
framework, which enables the representation of harmonic voltages and
currents as multidimensional vectors in Euclidean space. The use of the
geometric product allows to compute the geometric power multivector. The
proposed method is a generalization and extension of previous works that
have focused on single- phase and balanced three-phase systems. This
paper introduces a complete analysis of new power terms in arbitrary
multi- phase electrical systems entirely rooted on Geometric Algebra and
Symmetrical Components. Several synthetic and real-world examples are
presented to illustrate the novelty, effectiveness and accuracy of the
proposed approach. The results of this study contribute to the
development of a new geometric foundation for the power theory in
electrical engineering.%
\end{abstract}%



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