Instantaneous Frequency Estimation in Unbalanced Systems Using Affine Differential Geometry

TL;DR

This paper introduces a novel method for estimating instantaneous frequency in unbalanced electrical systems by leveraging affine differential geometry, providing a more accurate approach for single-phase and unbalanced conditions.

Contribution

It establishes a new link between electrical quantities and affine differential geometry, leading to an innovative frequency estimation formula tailored for unbalanced systems.

Findings

The proposed formula accurately estimates frequency in unbalanced systems.

Examples and real-world measurements validate the effectiveness of the method.

The approach enhances frequency analysis in single-phase and unbalanced power systems.

Abstract

The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on this link, a new instantaneous frequency estimation formula is proposed, which is particularly suited for unbalanced and single-phase systems. Several examples as well as measurements based on two real-world events illustrate the findings of the paper.