Equivalence between Geometric Frequency and Lagrange Derivative

TL;DR

This paper establishes a novel theoretical link between geometric frequency in electric systems and the Lagrange derivative in fluid dynamics, providing new insights for waveform analysis and system condition classification.

Contribution

It introduces the equivalence between geometric frequency and Lagrange derivative, bridging electric power analysis with fluid dynamics concepts for improved waveform distortion detection.

Findings

Decomposition of Lagrange derivative aids in waveform distortion identification

Numerical examples demonstrate classification of system operating conditions

Geometric frequency generalizes instantaneous frequency for electric power analysis

Abstract

The paper shows the equivalence between the geometric frequency of an electric quantity, namely, voltage and current, and the Lagrange derivative of a stream-line of a fluid. The geometric frequency is a concept recently proposed by the author and is a generalization of the instantaneous frequency, a quantity that is particularly important for the analysis and the control of electric power systems. On the other hand, the Lagrange derivative is mostly utilized in fluid dynamics and helps decomposing the time derivative into various components. The paper shows how these components relate to the elements of the geometric frequency. The paper also shows, through a variety of numerical examples, how the decomposition of the Lagrange derivative helps identifying the distortion of the waveform of a measured electric quantity and how this information can be utilized to classify system operating conditions.