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Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions

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

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

Abstract

Traditional electrical power theories and one of their most important concepts—apparent power—are still a source of debate, because they present several flaws that misinterpret the power-transfer and energy-balance phenomena under distorted grid conditions. In recent years, advanced mathematical tools such as geometric algebra (GA) have been introduced to address these issues. However, the application of GA to electrical circuits requires more consensus, improvements and refinement. In this paper, electrical power theories for single-phase systems based on GA were revisited. Several drawbacks and inconsistencies of previous works were identified, and some amendments were introduced. An alternative expression is presented for the electric power in the geometric domain. Its norm is compatible with the traditional apparent power defined as the product of the RMS voltage and current. The use of this expression simplifies calculations such as those required for current decomposition. This proposal is valid even for distorted currents and voltages. Concepts are presented in a simple way so that a strong background on GA is not required. The paper included some examples and experimental results in which measurements from a utility supply were analysed.

Suggested Citation

  • Francisco G. Montoya & Raúl Baños & Alfredo Alcayde & Francisco Manuel Arrabal-Campos & Javier Roldán-Pérez, 2021. "Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions," Mathematics, MDPI, vol. 9(11), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1295-:d:569232
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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    Cited by:

    1. Konrad Zajkowski & Stanisław Duer & Jacek Paś & László Pokorádi, 2023. "Cooperation of a Non-Linear Receiver with a Three-Phase Power Grid," Energies, MDPI, vol. 16(3), pages 1-17, February.

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