Quaternion-valued single-phase model for three-phase power system

Xiaoming Gou – Zhiwen Liu – Wei Liu – Yougen Xu – Jiabin Wang

   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.

Keywords: harmonics detection, Fourier transform, minimum variance distortionless response, multiple signal classification, quaternion, three-phase power system

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