Instantaneous Complex Phase and Frequency: Conceptual Clarification and Equivalence Between Formulations
Abstract
This letter seeks to clarify the different existing definitions of both instantaneous complex phase and frequency as well as their equivalence under standard modeling assumptions considered for transmission systems, i.e. balanced positive sequence operation, sole presence of electro-mechanical transient dynamics and absence of harmonics and interharmonics. To achieve this, the two fundamental definitions, i.e., those based on either the use of (i) analytic signals or (ii) space vectors, together with the premises used for their formulation, are presented and their relationship shown. Lastly, a unified notation and terminology to avoid confusion is proposed.
Fields of Study & Subjects
Acoustic Wave Phenomena Research
Quantum Electrodynamics and Casimir Effect
Quantum Mechanics and Non-Hermitian Physics
Publication details
- Journal / source
- IEEE Transactions on Power Systems
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Volume
- 41
- Issue
- 4
- Pages
- 3234–3237
- Publication date
- 27 April 2026