Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917356991676416 |
|---|---|
| author | Milano, Federico Tzounas, Georgios Dassios, Ioannis Murad, Mohammed Ahsan Adib Kërçi, Taulant |
| author_facet | Milano, Federico Tzounas, Georgios Dassios, Ioannis Murad, Mohammed Ahsan Adib Kërçi, Taulant |
| contents | This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the definition of IF which is based on the concept of analytic signals. The link between analytic signals and Clarke transform of three-phase voltages of an ac power system is also shown. Then the well-known five paradoxes of the IF are stated. In the second part of the paper, an approach based on a geometric interpretation of the frequency is proposed. This approach serves to revisit the five IF paradoxes and explain them through a common framework. The case study illustrates the features of the proposed framework based on a variety of examples and on a detailed model of the IEEE 39-bus system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12091 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency Milano, Federico Tzounas, Georgios Dassios, Ioannis Murad, Mohammed Ahsan Adib Kërçi, Taulant Signal Processing Systems and Control Differential Geometry This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the definition of IF which is based on the concept of analytic signals. The link between analytic signals and Clarke transform of three-phase voltages of an ac power system is also shown. Then the well-known five paradoxes of the IF are stated. In the second part of the paper, an approach based on a geometric interpretation of the frequency is proposed. This approach serves to revisit the five IF paradoxes and explain them through a common framework. The case study illustrates the features of the proposed framework based on a variety of examples and on a detailed model of the IEEE 39-bus system. |
| title | Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency |
| topic | Signal Processing Systems and Control Differential Geometry |
| url | https://arxiv.org/abs/2206.12091 |