An application of the spectral kurtosis to characterize power quality events q Juan José González de la Rosa a,b,⇑,1 , José María Sierra-Fernández a , Agustín Agüera-Pérez a , José Carlos Palomares-Salas a , Antonio Moreno-Muñoz a,c a Research Group PAIDI-TIC-168: Computational Instrumentation and Industrial Electronics (ICEI), Spain b University of Cádiz, Area of Electronics, EPSA, Av. Ramón Puyol S/N, E-11202 Algeciras, Cádiz, Spain c University of Córdoba, Area of Electronics, Campus de Rabanales, Leonardo da Vinci Building, E-14071 Córdoba, Spain article info Article history: Received 29 October 2012 Received in revised form 25 January 2013 Accepted 2 February 2013 Available online 15 March 2013 Keywords: Higher-Order Statistics (HOS) Frequency domain modeling Power Quality (PQ) Spectral Kurtosis (SK) abstract This paper deals with a novel application of the Spectral Kurtosis (SK) in power-quality modeling and analysis. The two major advantages of this three-spectral analysis are: robustness to noise and the capa- bility to detect nonlinearities, as impulsive-like signals. The first aim is to study some of the theoretical aspects of the SK estimation, performing a connection to the power-quality event analysis. Then, real-life situations’ performances are presented to correlate results with synthetics. Despite the fact the limited resolution in the frequency domain (to gain computation speed), the method presents an accuracy of 84% over real-life registers. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The higher-order statistics have been object of intensive basic and applied research during the past 10 years, due to their capa- bility to reject noise and to complement the classical second-or- der characterization [1]. One of the most useful tools is the fourth-order cumulant, in which the kurtosis is inspired. The kurtosis measures the peakedness of the probability distribution associated to the instantaneous amplitudes of the time-series measurements. Its complementary version in the frequency do- main, the Spectral Kurtosis (SK) can be initially defined as the kurtosis of its frequency components, and compares the variabil- ity in amplitude of the different spectral frequencies. Thus, this statistical parameter indicates how the impulsiveness of a signal varies with frequency. The SK is a fourth order spectrum whose prior estimators were introduced in the eighties for detecting transients in sonar processing [2], enhancing non-linearities and discovering hidden processes that in turn constitute a further support for the develop- ment of technology. The scientific community uses the SK for dis- tinguishing different types of signals [3]. Applications are biased in the field of machine diagnostics [4–6]; other works are found in the field of insect detection [7]. It has also been found that the spectral kurtosis can be used to form a filter to select out that part of the signal that is most impul- sive, considerably reducing the background noise and hence improving the diagnostic capability. The identification proved to be capable to identify quadratically coupled signals when the power-spectra failed [8]. Since Power-Quality (PQ) events give rise to sudden changes in the power line signal, this higher-order statistics (in particular the SK) are potentially useful to characterize the frequency bands asso- ciated to each type of the electrical anomaly. Following this philos- ophy, the subjacent goal of the paper is to use an estimator of the SK to measure the variability associated to each frequency compo- nent of the electrical signal. Consequently, a constant-amplitude (zero variability) single-frequency sinusoid exhibits a minimum SK value at this frequency; where as if the amplitude varies with time, the SK increases at this concrete frequency. More precisely, if the amplitude varies according to a normal distribution, the SK is zero. This philosophy has been brought to practice in the time-do- main by several notable works. For example, Bollen et al. used ad- vanced signal processing techniques to introduce new statistical features to PQ event detection [9]. In the same line, Gu and Bollen [10] found notable characteristics corresponding to power distur- bances in the time and frequency domains. It is also remarkable the work by Ribeiro et al. [11], which uses HOS to extract new time-domain features associated to electrical anomalies. HOS 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.02.002 q This work is funded and supported by the Spanish Ministry of Science and Innovation, via the project TEC2010-19242-C03-03 (SIDER-HOSAPQ). ⇑ Corresponding author at: University of Cádiz, Area of Electronics, EPSA, Av. Ramón Puyol S/N, E-11202 Algeciras, Cádiz, Spain. Tel./fax: +34 956028020. E-mail address: juanjose.delarosa@uca.es (J.J. González de la Rosa). URL: http://www.uca.es/grupos-inv/TIC168/ (J.J. González de la Rosa). 1 Main Researcher of the Research Unit PAIDI-TIC-168. Electrical Power and Energy Systems 49 (2013) 386–398 Contents lists available at SciVerse ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes