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

Author:

Montoya Francisco G.ORCID,Baños RaúlORCID,Alcayde AlfredoORCID,Arrabal-Campos Francisco M.ORCID,Roldán-Pérez JavierORCID

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.

Funder

Ministerio de Ciencia, Innovación y Universidades

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Geometric Procedure for Computing Differential Characteristics of Multi-phase Electrical Signals Using Geometric Algebra;Advanced Computational Applications of Geometric Algebra;2024

2. Survey of new applications of geometric algebra;Mathematical Methods in the Applied Sciences;2023-07-31

3. Instantaneous Reactive Power Theory in the Geometric Algebra Framework;Applied Sciences;2023-01-30

4. Analog Circuits;Mathematics;2022-12-12

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