Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply
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 system...
| Main Authors: | , , , , |
|---|---|
| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
MDPI
2021
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/11994 https://doi.org/10.3390/math9111259 |
| _version_ | 1789406547124682752 |
|---|---|
| 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 | 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. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-11994 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2021 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-119942023-04-12T19:31:39Z Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply 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 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. 2021-07-21T08:33:04Z 2021-07-21T08:33:04Z 2021-05-31 info:eu-repo/semantics/article 2227-7390 http://hdl.handle.net/10835/11994 https://doi.org/10.3390/math9111259 en https://www.mdpi.com/2227-7390/9/11/1259 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 Gil Montoya, Francisco Baños Navarro, Raúl Alcayde García, Alfredo Arrabal Campos, Francisco Manuel Roldán Pérez, Javier Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply |
| title | Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply |
| title_full | Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply |
| title_fullStr | Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply |
| title_full_unstemmed | Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply |
| title_short | Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply |
| title_sort | geometric algebra framework applied to symmetrical balanced three-phase systems for sinusoidal and non-sinusoidal voltage supply |
| topic | geometric algebra non-sinusoidal power clifford algebra power theory |
| url | http://hdl.handle.net/10835/11994 https://doi.org/10.3390/math9111259 |
| work_keys_str_mv | AT gilmontoyafrancisco geometricalgebraframeworkappliedtosymmetricalbalancedthreephasesystemsforsinusoidalandnonsinusoidalvoltagesupply AT banosnavarroraul geometricalgebraframeworkappliedtosymmetricalbalancedthreephasesystemsforsinusoidalandnonsinusoidalvoltagesupply AT alcaydegarciaalfredo geometricalgebraframeworkappliedtosymmetricalbalancedthreephasesystemsforsinusoidalandnonsinusoidalvoltagesupply AT arrabalcamposfranciscomanuel geometricalgebraframeworkappliedtosymmetricalbalancedthreephasesystemsforsinusoidalandnonsinusoidalvoltagesupply AT roldanperezjavier geometricalgebraframeworkappliedtosymmetricalbalancedthreephasesystemsforsinusoidalandnonsinusoidalvoltagesupply |