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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2112.03633 |
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| _version_ | 1866914413790887936 |
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| author | Milano, Federico Tzounas, Georgios Dassios, Ioannis Kerci, Taulant |
| author_facet | Milano, Federico Tzounas, Georgios Dassios, Ioannis Kerci, Taulant |
| contents | The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential geometry and provides a general framework for the definition of the time derivative of electrical quantities in stationary as well as transient conditions. As a byproduct, the proposed approach unifies and generalizes the time- and phasor-domain frameworks. Other noteworthy results are a new interpretation of the link between frequency and the time derivatives of voltage and current; and a definition of the rate of change of frequency that includes the novel concept of "torsional frequency." Several numerical examples based on balanced, unbalanced, harmonically-distorted and transient voltages illustrate the findings of the paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_03633 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Applications of the Frenet Frame to Electric Circuits Milano, Federico Tzounas, Georgios Dassios, Ioannis Kerci, Taulant Differential Geometry Systems and Control The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential geometry and provides a general framework for the definition of the time derivative of electrical quantities in stationary as well as transient conditions. As a byproduct, the proposed approach unifies and generalizes the time- and phasor-domain frameworks. Other noteworthy results are a new interpretation of the link between frequency and the time derivatives of voltage and current; and a definition of the rate of change of frequency that includes the novel concept of "torsional frequency." Several numerical examples based on balanced, unbalanced, harmonically-distorted and transient voltages illustrate the findings of the paper. |
| title | Applications of the Frenet Frame to Electric Circuits |
| topic | Differential Geometry Systems and Control |
| url | https://arxiv.org/abs/2112.03633 |