Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency
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...
| Prif Awduron: | , , , , |
|---|---|
| Fformat: | Erthygl |
| Iaith: | English |
| Cyhoeddwyd: |
IEEE
2022-01-01
|
| Cyfres: | IEEE Open Access Journal of Power and Energy |
| Pynciau: | |
| Mynediad Ar-lein: | https://ieeexplore.ieee.org/document/9809967/ |
| _version_ | 1828084462192164864 |
|---|---|
| author | Federico Milano Georgios Tzounas Ioannis Dassios Mohammed Ahsan Adib Murad Taulant Kerci |
| author_facet | Federico Milano Georgios Tzounas Ioannis Dassios Mohammed Ahsan Adib Murad Taulant Kerci |
| author_sort | Federico Milano |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T04:25:20Z |
| format | Article |
| id | doaj.art-c834b0e7e4cc4cff948bc6b4becccfd5 |
| institution | Directory Open Access Journal |
| issn | 2687-7910 |
| language | English |
| last_indexed | 2024-04-11T04:25:20Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Access Journal of Power and Energy |
| spelling | doaj.art-c834b0e7e4cc4cff948bc6b4becccfd52022-12-30T00:01:03ZengIEEEIEEE Open Access Journal of Power and Energy2687-79102022-01-01950151310.1109/OAJPE.2022.31868789809967Using Differential Geometry to Revisit the Paradoxes of the Instantaneous FrequencyFederico Milano0https://orcid.org/0000-0002-0049-9185Georgios Tzounas1https://orcid.org/0000-0002-1464-3600Ioannis Dassios2Mohammed Ahsan Adib Murad3https://orcid.org/0000-0002-5832-2980Taulant Kerci4https://orcid.org/0000-0003-4748-3399School of Electrical and Electronic Engineering, University College Dublin, Dublin 4, IrelandPower Systems Laboratory, ETH Zürich, Zürich, SwitzerlandSchool of Electrical and Electronic Engineering, University College Dublin, Dublin 4, IrelandDIgSILENT GmbH, Gomaringen, GermanyEirGrid plc, Dublin 4, IrelandThis 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.https://ieeexplore.ieee.org/document/9809967/Analytic signal (AS)Clarke transform (CT)differential geometryFourier transform (FT)harmonic analysis (HA)Hilbert transform (HT) |
| spellingShingle | Federico Milano Georgios Tzounas Ioannis Dassios Mohammed Ahsan Adib Murad Taulant Kerci Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency IEEE Open Access Journal of Power and Energy Analytic signal (AS) Clarke transform (CT) differential geometry Fourier transform (FT) harmonic analysis (HA) Hilbert transform (HT) |
| title | Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency |
| title_full | Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency |
| title_fullStr | Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency |
| title_full_unstemmed | Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency |
| title_short | Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency |
| title_sort | using differential geometry to revisit the paradoxes of the instantaneous frequency |
| topic | Analytic signal (AS) Clarke transform (CT) differential geometry Fourier transform (FT) harmonic analysis (HA) Hilbert transform (HT) |
| url | https://ieeexplore.ieee.org/document/9809967/ |
| work_keys_str_mv | AT federicomilano usingdifferentialgeometrytorevisittheparadoxesoftheinstantaneousfrequency AT georgiostzounas usingdifferentialgeometrytorevisittheparadoxesoftheinstantaneousfrequency AT ioannisdassios usingdifferentialgeometrytorevisittheparadoxesoftheinstantaneousfrequency AT mohammedahsanadibmurad usingdifferentialgeometrytorevisittheparadoxesoftheinstantaneousfrequency AT taulantkerci usingdifferentialgeometrytorevisittheparadoxesoftheinstantaneousfrequency |