  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.
