Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform

Francisco G. Montoya, Raúl Baños, Alfredo Alcayde, Francisco M. Arrabal-Campos and Javier Roldán-Pérez
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Francisco G. Montoya: Department of Engineering, University of Almeria, 04120 Almeria, Spain
Raúl Baños: Department of Engineering, University of Almeria, 04120 Almeria, Spain
Alfredo Alcayde: Department of Engineering, University of Almeria, 04120 Almeria, Spain
Francisco M. Arrabal-Campos: Department of Engineering, University of Almeria, 04120 Almeria, Spain
Javier Roldán-Pérez: Electrical Systems Unit, IMDEA Energy Institute, 28935 Madrid, Spain

Mathematics, 2022, vol. 10, issue 9, 1-17

Abstract: In this paper, power flows in electrical circuits are modelled in a mixed time-frequency domain by using geometric algebra and the Hilbert transform for the first time. The use of this mathematical framework overcomes some of the limitations of some of the existing methodologies, in which the so-called “active current” may not lead to the lowest Root Mean Square (RMS) current under distorted supply or unbalanced load. Moreover, this current may contain higher levels of harmonic distortion compared to the supply voltage. The proposed method can be used for sinusoidal and non-sinusoidal power supplies, non-linear loads and single- and multi-phase electrical circuits, and it provides meaningful engineering results with a compact formulation. It can also serve as an advanced tool for developing algorithms in the power electronics field. Several examples have been included to verify the validity of the proposed theory.

Keywords: geometric algebra; non-sinusoidal power; Clifford algebra; power theory; geometric electricity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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