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...
| Main Authors: | , , , , |
|---|---|
| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
MDPI
2022
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/13684 |
| _version_ | 1789406336954400768 |
|---|---|
| author | Gil Montoya, Francisco Baños Navarro, Raúl Alcayde García, Alfredo Arrabal Campos, Francisco Manuel Roldán Pérez, Javier |
| author_facet | Gil Montoya, Francisco Baños Navarro, Raúl Alcayde García, Alfredo Arrabal Campos, Francisco Manuel Roldán Pérez, Javier |
| author_sort | Gil Montoya, Francisco |
| collection | DSpace |
| 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. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-13684 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2022 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-136842023-10-25T11:09:51Z Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform Gil Montoya, Francisco Baños Navarro, Raúl Alcayde García, Alfredo Arrabal Campos, Francisco Manuel Roldán Pérez, Javier geometric algebra non-sinusoidal power Clifford algebra power theory geometric electricity 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. 2022-05-06T17:24:00Z 2022-05-06T17:24:00Z 2022-04-22 info:eu-repo/semantics/article 2227-7390 http://hdl.handle.net/10835/13684 10.3390/math10091419 en https://www.mdpi.com/2227-7390/10/9/1419 Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess MDPI |
| spellingShingle | geometric algebra non-sinusoidal power Clifford algebra power theory geometric electricity Gil Montoya, Francisco Baños Navarro, Raúl Alcayde García, Alfredo Arrabal Campos, Francisco Manuel Roldán Pérez, Javier Geometric Algebra Applied to Multiphase Electrical Circuits in Mixed Time–Frequency Domain by Means of Hypercomplex Hilbert Transform |
| 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 | http://hdl.handle.net/10835/13684 |
| work_keys_str_mv | AT gilmontoyafrancisco geometricalgebraappliedtomultiphaseelectricalcircuitsinmixedtimefrequencydomainbymeansofhypercomplexhilberttransform AT banosnavarroraul geometricalgebraappliedtomultiphaseelectricalcircuitsinmixedtimefrequencydomainbymeansofhypercomplexhilberttransform AT alcaydegarciaalfredo geometricalgebraappliedtomultiphaseelectricalcircuitsinmixedtimefrequencydomainbymeansofhypercomplexhilberttransform AT arrabalcamposfranciscomanuel geometricalgebraappliedtomultiphaseelectricalcircuitsinmixedtimefrequencydomainbymeansofhypercomplexhilberttransform AT roldanperezjavier geometricalgebraappliedtomultiphaseelectricalcircuitsinmixedtimefrequencydomainbymeansofhypercomplexhilberttransform |