Tracks of power quality transients in high order statistics spaces

This paper deals with the automatic classification of power quality transients according to their amplitudes and frequencies, and following the geometrical pattern previously established via higher-order statistical measurements. The clustering is achieved thanks to the third and fourth-order features associated to these electrical anomalies, which in turn are coupled to the 50-Hz power-line. The main contribution of the paper is the novel finding that the maxima and the minima of these higher-order cumulants distribute according families of curves of constant frequency or constant amplitude. A couple of extremes (min-max) of the higher-order statistical estimator belongs to a couple of curves (constant-frequency and constant-amplitude). The random grouping along each curve reveals the a priori hidden geometry, in turn linked to the subjacent electrical anomaly. The 2D (amplitude-frequency) regular surface grid in the input space experiments a transformation to both output spaces, which is developed via the higher-order non-linear mapping.