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.
This paper presents a novel model for transformer windings to accurately represent the duality between electrical and magnetic circuits. The model can be used for the calculation of high-frequency transients in power systems and the design of high-frequency transformers, for example, those to be used in solid-state (utility-grade) transformers and power electronic converters. Existing circuit models do not consider the flux linkage in the winding thickness in a physical (dual) way.