In this paper, we present a novel power-quality (PQ) event detection and classification method using higher order cumulants as the feature parameter, and quadratic classifiers as the classification method. We have observed that local higher order statistical parameters that are estimated from short segments of 50-Hz notch-filtered voltage waveform data carry discriminative features for PQ events analyzed herein. A vector with six parameters consisting of local minimas and maximas of higher order central cumulants starting from the second (variance) up to the fourth cumulant is used as the feature vector. Local vector magnitudes and simple thresholding provide an immediate event detection criterion. After the detection of a PQ event, local maxima and minima of the cumulants around the event instant are used for the event-type classification. We have observed that the minima and maxima for each statistical order produces clusters in the feature space. These clusters were observed to exhibit noncircular topology; hence, quadratic-type classifiers that require the Mahalanobis distance metric art! proposed. The events investigated and presented are line-to-ground arcing faults and voltage sags due to the induction motor starting. Detection and classification results obtained from an experimentally staged PQ event data set are presented.