This paper deals with the automatic classification of Power Quality (PQ) transients according to their amplitudes and frequencies, and following the geometrical pattern established via higher-order statistical measurements. The clustering is achieved thanks to the third and fourth-order features associated to the 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 to a family of curves, each of which associated to the transient's frequency. Given a statistical order, each point in a curve corresponds to a given initial amplitude of a transient, and to a couple of extreme values of the statistical estimator. The random grouping through each curve reveals the a priori hidden geometry, linked to the subjacent phenomenon. Once the geometry has been found, we show the computational intelligence modulus, based in Self-Organizing Maps, which performs satisfactory learning along each frequency curve. Performance of a six-neuron network with two different geometries is shown. The experience is a continuation of the research towards an automatic procedure for PQ event classification.
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