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Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply

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 Manuel Arrabal-Campos

    (Department of Engineering, University of Almeria, 04120 Almeria, Spain)

  • Javier Roldán Pérez

    (IMDEA Energy Institute, Electrical Systems Unit, 28935 Madrid, Spain)

Abstract

This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric algebra power theory (GAPoT) to multiple-phase systems. A definition of geometric apparent power for three-phase systems, that complies with the energy conservation principle, is also introduced. Power calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. By using the proposed framework, the current can be easily geometrically decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal that can be applied to systems under real operation conditions, where unbalance and asymmetry is considered.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1259-:d:566045
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    References listed on IDEAS

    as
    1. Francisco G. Montoya & Raul Baños & Alfredo Alcayde & Maria G. Montoya & Francisco Manzano-Agugliaro, 2018. "Power Quality: Scientific Collaboration Networks and Research Trends," Energies, MDPI, vol. 11(8), pages 1-16, August.
    2. Francisco G. Montoya & Alfredo Alcayde & Francisco M. Arrabal-Campos & Raul Baños, 2019. "Quadrature Current Compensation in Non-Sinusoidal Circuits Using Geometric Algebra and Evolutionary Algorithms," Energies, MDPI, vol. 12(4), pages 1-17, February.
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    Cited by:

    1. 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.

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