Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform
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-cal...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1419 |
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| author | Francisco G. Montoya Raúl Baños Alfredo Alcayde Francisco M. Arrabal-Campos Javier Roldán-Pérez |
| author_facet | Francisco G. Montoya Raúl Baños Alfredo Alcayde Francisco M. Arrabal-Campos Javier Roldán-Pérez |
| author_sort | Francisco G. Montoya |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T03:56:53Z |
| format | Article |
| id | doaj.art-b5c2b3b5c5c74fbab0b5274cec9eac1b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:56:53Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b5c2b3b5c5c74fbab0b5274cec9eac1b2023-11-23T08:44:01ZengMDPI AGMathematics2227-73902022-04-01109141910.3390/math10091419Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert TransformFrancisco G. Montoya0Raúl Baños1Alfredo Alcayde2Francisco M. Arrabal-Campos3Javier Roldán-Pérez4Department of Engineering, University of Almeria, 04120 Almeria, SpainDepartment of Engineering, University of Almeria, 04120 Almeria, SpainDepartment of Engineering, University of Almeria, 04120 Almeria, SpainDepartment of Engineering, University of Almeria, 04120 Almeria, SpainElectrical Systems Unit, IMDEA Energy Institute, 28935 Madrid, SpainIn 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.https://www.mdpi.com/2227-7390/10/9/1419geometric algebranon-sinusoidal powerClifford algebrapower theorygeometric electricity |
| spellingShingle | Francisco G. Montoya Raúl Baños Alfredo Alcayde Francisco M. Arrabal-Campos Javier Roldán-Pérez Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform Mathematics geometric algebra non-sinusoidal power Clifford algebra power theory geometric electricity |
| title | Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform |
| title_full | Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform |
| title_fullStr | Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform |
| title_full_unstemmed | Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform |
| title_short | Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform |
| title_sort | geometric algebra applied to multiphase electrical circuits in mixed time frequency domain by means of hypercomplex hilbert transform |
| topic | geometric algebra non-sinusoidal power Clifford algebra power theory geometric electricity |
| url | https://www.mdpi.com/2227-7390/10/9/1419 |
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