Quaternion-Valued Single-Phase Model for Three-Phase Power Systems

TL;DR

This paper introduces a quaternion-valued model for three-phase power systems that enhances harmonic distortion detection by mapping all harmonic frequencies into the quaternion domain, overcoming limitations of traditional methods.

Contribution

The paper proposes a novel quaternion-valued model replacing Clarke's transformation for improved harmonic detection in three-phase systems.

Findings

Quaternion model maps all harmonic frequencies into the quaternion domain.

The model detects zero sequence voltages that traditional methods miss.

Simulations demonstrate the effectiveness of the quaternion-based approach.

Abstract

In this work, a quaternion-valued model is proposed in lieu of the Clarke's \alpha, \beta transformation to convert three-phase quantities to a hypercomplex single-phase signal. The concatenated signal can be used for harmonic distortion detection in three-phase power systems. In particular, the proposed model maps all the harmonic frequencies into frequencies in the quaternion domain, while the Clarke's transformation-based methods will fail to detect the zero sequence voltages. Based on the quaternion-valued model, the Fourier transform, the minimum variance distortionless response (MVDR) algorithm and the multiple signal classification (MUSIC) algorithm are presented as examples to detect harmonic distortion. Simulations are provided to demonstrate the potentials of this new modeling method.