HOS-based method for classification of power quality disturbances D.D. Ferreira, A.S. Cerqueira, C.A. Duque and M.V. Ribeiro Presented is a novel method for disturbance classification using a higher-order statistics-based technique for extracting a reduced and representative event signature vector and a neural network for classifi- cation. The signature vectors provide enough separability among classification regions, resulting in a classification rate of 100% for the validation events set. Introduction: Power quality (PQ) is directly associated with the quality of the voltage signal waveform signal at the analysis point [1]. Following this definition, the main PQ events are transients, long and short voltage variations, flickers, harmonics, inbalances, etc. [1]. PQ analysis is a research field increased attention in that has received recent years, mainly for the following reasons: 1. the fast expansion of power electronics devices leads to a wide diffusion of nonlinear, time- variant loads in the power system, which causes loss in the quality of power; 2. the growing use of accurate electronic devices requiring high power quality supplies; 3. the need to localise the disturbance sources in order to quickly solve the power quality problem; and 4. the large amount of power quality data recorded that demands automatic classification. This Letter focuses on the PQ events classification and proposes the use of a higher-order statistics (HOS)-based technique, such as cummu- lants, applied over the voltage waveform for feature extraction. The use of cummulants appears to be interesting because they are not sensitive to background Gaussian noise and they are also useful in problems where either non-Gaussianity or nonlinearities are involved [2]. The classifi- cation is performed with an artificial neural network [3]. The proposed method is compared with two other methods [4, 5]. The main advan- tages of the proposed method are the non-sensibility to Gaussian back- ground noise, the simplification of the classification algorithm and the performance improvement. Proposed method: The block diagram of the proposed method is por- trayed in Fig. 1. Note that the feature extraction is performed over the voltage waveform containing the PQ event and the classification is per- formed over the selected features. neural network for classification HOS for feature extraction PQ event voltage waveform classification result (FDR) feature selection Fig. 1 Proposed system for power quality event classification The HOS-based technique is used for feature extraction from the voltage waveform. So far it has been shown that higher-order stat- istics-based techniques are more appropriate to deal with non- Gaussian processes and nonlinear systems than the second-order ones [2]. In fact HOS-based signature vectors of voltage events provide classification regions in a hyperspace expanded by the very well defined signature vectors. The expressions of the diagonal slice of second- and fourth-order cummulants of a zero mean x(n), where x(n) is a vector containing N samples of the event, are defined by [6]: ^ C 2;x ðiÞ¼ 1 N P N1 n¼0 xðnÞxðmodðn þ i; N ÞÞ ð1Þ and ^ C 4;x ðiÞ¼ 1 N P N1 n¼0 xðnÞx 3 ðmodðn þ i; N ÞÞ  3 1 N 2 P N1 n¼0 xðnÞxðmodðn þ i; N ÞÞ P N1 n¼0 x 2 ðnÞ ð2Þ where i ¼ 0, 1, 2, ... , N 2 1 and the function mod(a,b) is the modulus, returning the integer remainder after dividing a into b. To reduce the dimensions of the extracted features and consequently the computational complexity and processing time, the Fisher’s discri- minant ratio (FDR) [6] is used, aiming at the choice of a representative and finite set of features among those obtained by HOS that provides a good separability between two distinct classes. The cost vector function of the FDR is given by J c ¼ðm 1  m 2 Þ 2  1 D 2 1 þ D 2 2 ð3Þ where J c ¼ [J 1 ... J L ] T , L is the total number of features, m 1 and m 2 , and D 1 2 and D 2 2 are the mean and variance of the features vectors p 1,k e p 2,k , k ¼ 1, 2, ... , M p , and M p denotes the total number of feature vectors (number of events used for the feature selection).  refers to the Hadamard product. From (3), it is understandable that the ith element of the feature vector providing the greatest values of J i are selected for use in the classifi- cation. Therefore, it is possible to reduce the dimensions of the data pre- sented to the classifier to simplify the classification algorithm. Thus, a simple multilayer feed-forward neural network is used for event classi- fication owing to the good performance achieved for nonlinear pattern recognition [3] and the low computational cost during operation. Methodology and system design: In this Letter, five classes of PQ events are considered: harmonics (C1), sags/swells (C2), oscillator transient (C3), notches (C4) and spikes (C5). The events were simulated by soft- ware following the definitions found in [1, 4, 5] with a sampling fre- quency ( fs) of 15360 samples per second and with a total length (N ) of 1024 samples. 500 events were generated per class and were equally divided into two groups, one for the system design and the other for system validation. All events were generated with an additive Gaussian white noise with a SNR of 30 dB. The first step in designing the system is to compute the diagonal slices of the second- and fourth-order cummulants for the N samples of each event according to (1) and (2), respectively. Therefore, for each event, a total of 2N samples from the two cummulants for each event are obtained. Next, the FDR was computed considering one class against the other. Therefore, for each class a vector J c with 2N elements is obtained. Taking the greatest value of J c related to each cummulant, a total of two parameters for each class are selected, one from second- order and one from fourth-order, giving a total of ten parameters for each event. Therefore, the original dimension of each event was reduced from 1024 to 10. This procedure is performed during design. Fig. 2 shows the two selected parameters (second and fourth cummu- lants) for each class of PQ disturbances considered, showing the separ- ability between these classes. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 feature space C 2,x C 4,x notch harmonic sag/swell oscil. trans. spike 0.95 0.96 0.97 0.98 0.99 1 0.3 0.4 0.5 0.6 0.7 feature space zoom C 2,x Fig. 2 Feature space from classes of PQ disturbances using selected parameters from diagonal slice of cummulants The ten selected parameters are finally presented to a multilayer feed- forward neural network for event classification. During the system design, the neural network is trained using the back-propagation algori- thm. The training process is stopped when the desired classification per- formance is achieved. The implemented system can be seen in Fig. 3. First, the selected samples of the second- and fourth-order cummulants of the detected PQ event with length N ¼ 1024 ( fs ¼ 15360 samples/s) are computed resulting in the feature vector with length N ¼ 10. The feature vector feeds the previously trained neural network with three layers, the input layer with ten input nodes, the hidden layer with five neurons and the output layer also with five neurons (five classes). The highest value indi- cates the event class at the neural network output. ELECTRONICS LETTERS 29th January 2009 Vol. 45 No. 3