IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009
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Signal Decomposition With Reduced Complexity for Classification of Isolated and Multiple Disturbances in Electric Signals Eduardo Pestana de Aguiar, Student Member, IEEE, Cristiano Augusto Gomes Marques, Carlos Augusto Duque, Member, IEEE, and Moisés Vidal Ribeiro, Member, IEEE
Abstract—In a previous work, the authors discussed and introduced a technique for the classification of isolated and multiple disturbances in electric signals. However, in that work, the decomposition of the electric signal into the fundamental, harmonic, and error component can be a very difficult task to be accomplished in real time. In this regards, this contribution proposes and analyzes the decomposition of electric signals into fundamental and error components. For each component, higher order statistics (HOS)based features are selected and extracted and feed Bayesian classifiers that are designed for each class of disturbance. Comparison results with a standard HOS-based classification technique indicate that the proposed technique can offer improved performance not only for isolated disturbance, but also for multiples ones. Index Terms—Feature evaluation and selection, feature extraction or construction, pattern recognition, signal processing.
I. INTRODUCTION
C
LASSIFICATION of disturbances in electric signals has been researched for a long time. International institutes are continually introducing procedures to classify all disturbances in order to relate them to some specific underlying causes in power systems. The need for new procedures to classify disturbances in electric signals is due to the increasing complexity of power systems that are yielded by new distribution and nonlinear generation plants, nonlinear loads, and interconnection of different power grids. As a result, the occurrence of multiple disturbances in the electric signal must be addressed to push forward the next power system monitoring functionalities. The new power system monitoring concept will be one of the key tools for the widespread use of the smart-grid concept in power systems. In [1] and [2], techniques were introduced to classify isolated and multiple disturbances in electric signals. The technique discussed in [1] is applied to several classes of isolated and multiple disturbances while in [2], a proposal to classify few ones is addressed. The performance highlighted in [1] indicates that the decomposition of electric signals into few primitive components, such as fundamental, harmonic, and transient can improve performance. However, one can note that such decom-
Manuscript received November 05, 2008. Current version published September 23, 2009. This work was supported in part by CAPES, in part by CNPq, in part by FAPEMIG, and in part by FINEP from Brazil. Paper no. PESL-00132-2008. E. P. de Aguiar, C. A. Duque, and M. V. Ribeiro are with the Electrical Engineering Department, Federal University of Juiz de Fora, Juiz de Fora, MG 36 036 330, Brazil (e-mail:
[email protected];
[email protected];
[email protected]). C. A. G. Marques is with COPPE/Federal University of Rio de Janeiro, Rio de Janeiro 68504, Brazil. He is also with the Federal University of Juiz de Fora, Juiz de Fora, MG 36 036 330, Brazil (e-mail:
[email protected]). Digital Object Identifier 10.1109/TPWRD.2009.2028750
position of electric signals is a very difficult task to be accomplished. In fact, if the number of harmonics is unknown or if the number is large, then the signal decomposition to be accomplished in real time becomes a difficult task. One can conclude that the applicability of [1] will have some limitations. Another very timely issue is to check whether decomposed signals can offer better performance compared to the situation when only the acquired signal is applied to classify disturbances. Some previous contributions indicate the suitability of decomposed signals for disturbance classification. To address the aforementioned issues, the decomposition of electric signals into two components is discussed, such as: 1) fundamental and 2) error. In that case, the decomposition can be easily accomplished by using a very simple filtering technique. In addition, simulation results reveal that classification by using information from the decomposed signal generates better results than classification performance over the nondecomposed signal. II. PROPOSED TECHNIQUE The discrete version of monitored power-line signals is disamples. The discrete vided into nonoverlapped frames of sequence in a frame can be expressed as an additive contribution of several types of phenomena (1) where , is the sampling period, , , , , and and the sequences denote the power-supply signal (or fundamental component), harmonics, interharmonics, transient, and background noise, reis decomposed into and spectively. Assuming that , then vectors , , and can be con, , and , respectively. The stituted by samples of standard scheme for classifying disturbances in electric signals is portrayed in Fig. 1. In this scheme, features are directly extracted from vector . On the other hand, the proposed scheme for classification of disturbance with the decomposed signals is shown in Fig. 2. In this scheme, features are independently extracted from vectors and and, then, applied to classifiers. The following tools 2) to 4) were applied to generate the results for the standard technique while for the proposed technique, the tools 1) to 4) were applied: 1) signal decomposition of vector in vectors and with an infinite-impulse-response (IIR) notch filter [3]; 2) feature extraction based on higher order statistics (HOS) [4] and their modified versions as introduced in [1]; 3) feature selection with Fisher discriminant ratio [5]; 4) Bayes classifier based on maximum-likelihood (ML) criterion and Gaussian assumption [6].
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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 24, NO. 4, OCTOBER 2009
TABLE I CLASSIFICATION PERFORMANCE OF ISOLATED DISTURBANCES (IN PERCENT) Fig. 1. Standard technique for disturbance classification.
Fig. 2. Proposed technique for disturbance classification. TABLE II CLASSIFICATION PERFORMANCE OF MULTIPLE DISTURBANCES (IN PERCENT)
III. NUMERICAL RESULTS To verify the performance of the proposed and standard techniques in order to classify single and multiple disturbances, simulations were carried out with several waveforms of voltage 256 signals generated with a sampling rate equal to 60 Hz, 1024 samples or four cycles for classification, and a signal-to-noise ratio (SNR) that is equal to 30 dB. The forgetting factor of notch IIR filter was 0.991. The number of samples for each class of disturbance is 500. The number of extracted features provided by the FDR was three for both techniques. The selected primitive patterns were swell, sag, interruption, flicker, damped oscillation, impulsive transient, notch, and harmonic. The multiple patterns were sag+harmonic+flicker, swell+harmonic+flicker, sag+harmonic, sag+flicker, swell+harmonic, and swell+flicker. The results achieved with the proposed and standard techniques are presented in Tables I and II, respectively. The efficiency is calculated by (2) is the classification ratio for the th pattern and where is the total number of patterns. Note that Table II shows results related to the situation where a reduced set of multiple and isolated disturbances is in the electric signals. In both tables, the fourth column shows the classification results when the signal is ideally decomposed and then applied to the classifier. The results are very good because the transient related to the filtering technique applied to signal decomposition does not appears in the decomposed disturbances. This result indicates that much better performance can be achieved if signal decomposition can be improved. Based on the reported results, one can verify that the proposed technique provides better results than the standard technique if isolated and the selected set of multiple disturbances occurs in electric signals.
IV. CONCLUSION This letter addressed a very simple approach for disturbance classification that is derived from [1]. The attained results indicate that the decomposition of the electric signal for further disturbance classification design can offer better results than designing classification directly from the electric signals. Additionally, the proposed technique is more simple than that in [1] for signal decomposition. Last, but not least, the attained results reveal that improvement in terms of classification ratio will be observed if powerful and nonlinear classifiers are applied. REFERENCES [1] M. V. Ribeiro and J. L. R. Pereira, “Classification of single and multiple disturbances in electric signals,” EURASIP J. Advances Signal Process., vol. 2007, no. Article ID 56918, 2007, 18 pp. [2] H. He and J. A. Starzyk, “A self-organizing learning array system for power quality classification based on wavelet transform,” IEEE Trans. Power Del., vol. 21, no. 1, pp. 286–295, Jan. 2006. [3] S. K. Mitra, Digital Signal Processing, 3rd ed. New York: McGrawHill, 2005. [4] J. M. Mendel, “Tutorial on higher-order statistics (spectra) in signal processing and system theory: Theoretical results and some applications,” Proc. IEEE, vol. 79, no. 3, pp. 278–305, Mar. 1991. [5] A. K. Jain, R. P. W. Duin, and J. Mao, “Statistical pattern recognition: A review,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 22, no. 1, pp. 4–37, Jan. 2000. [6] S. Theodoridis and K. Koutroumbas, Pattern Recognition. San Diego, CA: Academic Press, 1999.
