Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions
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 too...
| Main Authors: | , , , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
| Published: |
MDPI
2021
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| Online Access: | http://hdl.handle.net/10835/11985 https://doi.org/10.3390/math9111295 |
| _version_ | 1789406375335428096 |
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| 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 | 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. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-11985 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2021 |
| publisher | MDPI |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-119852023-04-12T19:29:43Z Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions 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 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. 2021-07-21T07:53:59Z 2021-07-21T07:53:59Z 2021-06-04 info:eu-repo/semantics/article 2227-7390 http://hdl.handle.net/10835/11985 https://doi.org/10.3390/math9111295 en https://www.mdpi.com/2227-7390/9/11/1295 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 Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions |
| title | Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions |
| title_full | Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions |
| title_fullStr | Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions |
| title_full_unstemmed | Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions |
| title_short | Vector Geometric Algebra in Power Systems: An Updated Formulation of Apparent Power under Non-Sinusoidal Conditions |
| title_sort | vector geometric algebra in power systems: an updated formulation of apparent power under non-sinusoidal conditions |
| topic | geometric algebra non-sinusoidal power Clifford algebra power theory |
| url | http://hdl.handle.net/10835/11985 https://doi.org/10.3390/math9111295 |
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