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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Francisco G. Montoya & Raúl Baños & Alfredo Alcayde & Francisco M. Arrabal-Campos & Javier Roldán-Pérez, 2022. "Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform," Mathematics, MDPI, vol. 10(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1419-:d:800224
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    References listed on IDEAS

    as
    1. Francisco G. Montoya & Raúl Baños & Alfredo Alcayde & Francisco Manuel Arrabal-Campos & Javier Roldán Pérez, 2021. "Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
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    Cited by:

    1. Luigi Fortuna & Arturo Buscarino, 2022. "Analog Circuits," Mathematics, MDPI, vol. 10(24), pages 1-4, December.
    2. Ahmad Hosny Eid & Francisco G. Montoya, 2024. "Developing GA-FuL: A Generic Wide-Purpose Library for Computing with Geometric Algebra," Mathematics, MDPI, vol. 12(14), pages 1-33, July.

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