Power Quality – Monitoring, Analysis and Enhancement 112 2 22 2 1 2 0 , imj N mn N m nmn SjT H e e NT NT π π − − = +  =    (18) where n≠0 and H[n/NT] is the Fourier transform of time series. The STFT transform limitation is the fixed window width, chosen a priori, for analysis of nonstationary signals containing low-frequency and high-frequency components. Consequently, the frequency-time resolution is fixed too and is difficult to analyze a sinusoidal signal of low frequecy (for instance the signal from power supply network) affected by a high frequency disturbance (for instance a transient phenomenon). The wavelet transform limitations are: low resolution for low-frequency components, the decomposition frequency bands are fixed, noise sensitivity. The S transform is an extension of the wavelet transform resulted using a phase correction which provides superior resolution. Applying DST on a signal the result is a matrix within the rows are frequences and the columns are time values. 5.1 Using the S-transform To ilustrate the ability of the ST to detect, localize and quantify power quality disturbances are considered two signals. First signal is afected by a voltage swell (low-frequency components) and the second by an impulsive transient (high-frequency components). Figure 11 shows the 3D ST plots for both signals. From the 3D plots can be observed the amplitude variations of the frequency spectral components in the signals. Fig. 11. S-transform 3D representation Methodes of Power Quality Analysis 113 Figure 12 presents the ST of a clean signal and six types of power quality disturbances (voltage sag, voltage swell, voltage interruption, voltage harmonics, impulsive transient and oscillatory transient): a) the signal, b) the normalized time-frequency contour of ST, c) the maximum of amplitude-time characteristic of S transform and d) the maximum of amplitude-frequency characteristic of of S transform. From visual inspection of these plots are obtained amplitude, frequency and time information in order to detect, localize and classify the disturbance. Power Quality – Monitoring, Analysis and Enhancement 114 Fig. 12. S-transform Figure 12 shows that the maximum of amplitude-time characteristic of S transform is constant for the clean signal and voltage harmonics and the maximum of amplitude- frequency characteristic of S transform reflects the changes in frequency domain due the presence of disturbances. 6. Impulsive transient characterization The power quality disturbances that may occur in power supply networks are classified in various categories (Dungan, 2004): transient phenomenons, short duration variations, long duration variations, voltage imbalances, waveform distortions, power frequency variations and flickers. Transient phenomenons are sudden and short-duration change in the steady-state condition of the voltage, current or both. These phenomenons are classified in two categories: impulsive and oscillatory transient. The first category has exponential rise and falling fronts and is characterized by magnitude, rise time (the time required for a signal to rise from 10% to 90% of final value), decay time (the time until a signal is greater than ½ from its magnitude) and its spectral content. In order to calculate the rise time for an impulsive transient (biexponential impulse) is proposed a simple algorithm. First are calculated 10%, 90% and 50% of peak amplitude. Than is necessary a loop to find the sample position of the previous values in waveform. Finally the rise time and the decay time are calculated as the difference between the positions found below. In Fig. 13 Rise time c is calculated using the previously described method and Rise time is the exact value of rise time. In Fig. 14 Decay time c is calculated also using the previous algorithm and Decay time is the exact value of decay time. The result of the rise time calculation depends on sampling frequency. Table 2 contains the informations corresponding to a biexponential impulse (Fig. 13) when the sampling frequency is increased six times: Ve represents the exact value of rise time, V1 and V2 are the values obtained at low sampling rate and respectively at increased sampling rate, Er1 and Er2 are the errors between V1 and V2 and respectively Ve and Er1/Er2 is the last column of Table 2. Methodes of Power Quality Analysis 115 Fig. 13. Influence of sample rate on accuracy of rise time calculation Ve V1 V2 Er1 [%] Er2 [%] Er1/Er2 Tcr [ms] 31.03 35.3 32 13.761 3.13 4.396 Table 2. Rise time calculation Fig. 14. Influence of sample rate on accuracy of decay time calculation 7. Conclusion Nowadays, the researchers must to choose the most appropiate method to analyse the raw data. The main objectiv is features extraction of power quality disturbances in order to achive automatic disturbance recognition. A comparative study between DFT, STFT, DWT and ST is presented accompany with applications in power quality disturbances detection. Supplementary, a solution to improve the STFT analysis is described. Impulsive transients characterization is also presented. Power Quality – Monitoring, Analysis and Enhancement 116 8. References Amaris, H. ; Alvarez, C. ; Alonso, M. ; Florez, D. ; Lobos, T. ; Janik, P.; Rezmer, J. ; Waclawek, Z. (2009). Computation of Voltage Sag Initiation with Fourier based Algorithm, Kalman Filter and Wavelets, Proceedings of IEEE Bucharest PowerTech. Azam, M. S.; Tu, F.; Pattipati, K. R.; Karanam, R. (2004). A Dependency Model Based Approach for Identifying and Evaluating Power Quality Problems, IEEE Transactions on Power Delivery 19(3) , pp. 1154-1166. Barrera Nunez, V. ; Melendez Frigola, J. ; Herraiz Jaramillo, S. (2008). A Survey on Voltage Dip Events in Power Systems, Proceedings of the Internatiional Conference on Renewable Energies and Power Quality. Bollen, M. H. J.; Gu, I. Y. H. (2006). Signal Processing of Power Quality Disturbances, John Wiley & Sons. Castro, R.; Diaz, H. (2002). An Overview of Wavelet Transform Application in Power Systems, Proceedings of the 14 th Power Systems Computation Conference. Chen, S.; Zhu, Y. (2007). Wavelet Transform for Processing Power Quality Disturbances, EURASIP Journal on Advances in Signal Processing. Chilukuri, M. V.; Dash, P. K. (2004). Multiresolution S-Transform-based fuzzy recognition system for power quality events, IEEE Transaction on Power Delivery 19(1), pp. 323- 330. Cornforth, D. ; Middleton, R. ; Tusek, J. (2000). Visualisation of Electrical Transients using the Wavelet Transform, Proceedings of the Internatiional Conference on Advances in Intelligent Systems. Dash, P. K.; Nayak, M ; Senapati, M. R.; Lee, I. W. C (2007). Mining for similarities in time series data using wavelet-based feature vectors and neural networks, Engineering Applications of Artificial Intelligence 20, pp. 185-201. Dehghani, M. D. (2009). Comparison of S-transform and Wavelet Transform in Power Quality Analysis, World Academy of Science, Engineering and Technology 50, pp. 395- 398. Driesen, J. ; Belmans, R. (2002). Time-Frequency Analysis in Power Measurement using Complex Wavelets, Proceedings of the IEEE International Symposium on Circuits and Systems. Driesen, J.; Belmans, R. (2003). Wavelet-based Power Quantification Approaches, IEEE Transactions on Instrumentation and Measurement 52(4), pp. 1232-1238. Duarte, G., Cesar; Vega, G., Valdomiro; Ordonez, P., Gabriel (2006). Automatic Power Quality Disturbances Detection and Classification Based on Discrete Wavelet Transform and Artificial Intelligence, Proceedings of the IEEE PES Transmission and Distribution Conference and Exposition Latin America. Dungan, R. C.; McGranaghan M. F., Santoso S., Beaty H. W. (2004). Electrical Power System Quality, McGraw-Hill. Eldin, E. S. M. T. (2006). Characterisation of power quality disturbances based on wavelet transforms, International Journal of Energy Technology and Policy 4(1-2), pp. 74-84. Fernandez, R. M. C.; Rojas, H. N. D. (2002). An overview of wavelet transforms application in power systems, Proceedings of the 14 th Power System Computational Conference. Gang, Z. L. (2004). Wavelet-based neural network for power disturbance recognition and classification, IEEE Transaction on Power Delivery 19(4), pp. 1560-1568. Methodes of Power Quality Analysis 117 Gaouda, A. M. ; Sultan, M. R. ; Chikhani, A. Y. (1999). Power Quality Detection and Classification Using Wavelet-Multiresolution Signal Decomposition, IEEE Transaction on Power Delivery 14(4), pp. 1469-1476. Gargoom, A. M.; Ertugrul, N., Soong, W. L. (2008). Automatic Classification and Characterization of Power Quality Events, IEEE Transactions on Power Delivery 23(4), pp. 2417-2425. He, H. ; Shen, X., Starzyk, J. A. (2009). Power quality disturbances analysis based on EDMRA method, International Journal of Electrical Power and Energy Systems 31, pp. 258-268. Ignea, A. (1998). Introducere în compatibilitatea electromagnetică, Editura de Vest Jena, G. ; Baliarsingh , R. ; Prasad, G. M. V. (2006). Application of S Transform in Digital Signal/Image, Proceedings of the National Conference on Emerging Trends in Electronics & Communication. Khan, U. N. (2009). Signal Processing Techniques used in Power Quality Monitoring, Proceedings of the International Conference on Environment and Electrical Engineering. Leonowicz, Z. ; Lobos, T. ; Wozniak, K. (2009). Analysis of non-stationary electric signals using the S-transform, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 28(2), pp. 204-2010. Nath, S. ; Dey, A. ; Chakrabarti, A. (2009). Detection of Power Quality Disturbances using Wavelet Transform, Journal of World Academy of Science, Engineering and Technology 49, pp. 869-873. Panigrahi, B. K. ; Hota, P. K. ; Dash, S. (2004). Power Quality Analysis Using Phase Correlated Wavelet Transform, Iranian Journal of Electrical and Computer Engineering 3(2), pp. 151-155. Reddy, J. B. ; Mohanta, D. K. ; Karan, B. M. (2004). Power System Disturbance Recognition Using Wavelet and S-Transform Techniques, International Journal of Emerging Electric Power Systems 1(2). Resende, J. W. ; Chaves , M. L. R. ; Penna, C. (2001). Identification of power disturbances using the MATLAB wavelet transform toolbox, Proceedings of the International Conference on Power Systems Transients. Samantaray, S. R. ; Dash, P. K. ; Panda, G. (2006). Power System Events Classification Using Pattern Recognition Approach, International Journal of Emerging Electric Power Systems 6(1). Saxena, D. ; Verma, K. S. ; Singh, S. N. (2010). Power quality event classification: an overview and key issues, International Journal of Engineering, Science and Technology 2(3). Stockwell, R. G. (2007). A basis for efficient representation of the S-transform, Digital Signal Processing 17(1), pp. 371-393. Uyar, M. ; Yildirim, S. ; Gencoglu, M. T. (2004). An expert system based on S-transform and neural network for automatic classification of power quality disturbances, Expert Systems with Applications 36, pp. 5962-5975. Vega, G. V. ; Duarte G. C. ; Ordóñez P. G. (2009). Automatic Power Quality Disturbances Detection and Classification Based on Discrete Wavelet Transform and Support Vector Machines, Proceedings of the 20th International Conference and Exhibition Electicity Distribution. Power Quality – Monitoring, Analysis and Enhancement 118 Vetrivel, A. M. ; Malmurugan, N. ; Jovitha, J. (2009). A Novel Method of Power Quality Disturbances Measures Using Discrete Orthogonal S Transform (DOST) with Wavelet Support Vector Machine (WSVM) Classifier, International Journal of Electrical and Power Engineering 3(1), pp. 59-68. Yong, Z; Hao-Zhong C.; Yi-Feng, D.; Gan-Yun, L.; Yi-Bin, S. (2005). S-Transform-based classification of power quality disturbance signals by support vector machines, Proceedins of the CSEE, pp. 51-56. Zhu, T. X. ; Tso, S. K. ; Lo, K. L. (2004). Wavelet-Based Fuzzy Reasoning Approach to Power- Quality Disturbance Recognition, IEEE Transaction on Power Delivery 19(4), pp. 1928-1935. 7 Pre-Processing Tools and Intelligent Systems Applied to Power Quality Analysis Ricardo A. S. Fernandes 1 , Ricardo A. L. Rabêlo 1 , Daniel Barbosa 2 , Mário Oleskovicz 1 and Ivan Nunes da Silva 1 1 Engineering School of São Carlos, University of São Paulo (USP), 2 Salvador University (UNIFACS) Brazil 1. Introduction In the last few years the power quality has become the target of many researches carried out either by academic or by utility companies. Moreover, a desired good power quality is essential for the Power Distribution System (PDS). The PDS can have (or impose) inherent operational conditions, that affect frequency and three-phase voltage signals. Among the main disturbances that indicate a poor power quality, the following can be highlighted: voltage sag/swell, overvoltage, undervoltage, interruption, oscillatory transient, noise, flicker and harmonic distortion (Dugan et al., 2003). Actually, in literature, a diversity of papers can be found concerning detection and identification of power quality disturbances by applying intelligent systems, such as Artificial Neural Networks (ANN) (Janik & Lobos, 2006; Oleskovicz et. al., 2009; Jayasree, Devaraj & Sukanesh, 2010) and Fuzzy Inference Systems (Zhu, Tso & Lo, 2004; Hooshmand & Enshaee, 2010; Meher & Pradhan, 2010; Behera, Dash & Biswal, 2010). However, only some papers use data pre-processing tools before the application of intelligent systems. Among these papers, the use of Discrete Wavelet Transform (DWT) (Zhu, Tso & Lo, 2004; Uyar, Yildirim & Gencoglu, 2008; Oleskovicz et. al., 2009) and Discrete Fourier Transform (DFT) (Zhang, Li & Hu, 2011) can be highlighted in the pre-processing stage. According to the literature, it should also be mentioned that the pre-processing tools help to ensure a better detection and identification of disturbances in the power quality context. In Hooshmand & Enshaee (2010), the authors propose a new method for detecting and classifying power quality disturbances. However, this method can be used both for the occurrence of one and multiple disturbances. This is a method that uses techniques for data pre-processing combined with intelligent systems. In this case, the authors extracted features of a time-varying voltage signal, such as: • Fundamental component; • Phase angle shift; • Total harmonic distortion; • Number of the maximums of the absolute value of wavelet coefficients; • Calculation of energy of the wavelet coefficients; Power Quality – Monitoring, Analysis and Enhancement 120 • Number of zero-crossing of the missing voltage; and • Number of peaks of Root Mean Square (RMS) value. After the pre-processing step, the authors conducted the detection and classification of disturbances by means of an hybrid intelligent system where two fuzzy systems were developed (one being the detector and other the classifier of the disturbances). However, what classifies this intelligent system as hybrid is the use of Particle Swarm Optimization (PSO) to tune/adjust the membership functions. The results obtained tries to validate the proposed methodology, where it was found satisfactory correctness rate. In the paper done by Jayasree, Devaraj & Sukanesh (2010), the authors employ the Hilbert Transform (HT) as pre-processing stage instead of the Fourier or Wavelet Transforms, which are commonly used for the same purpose (detect and/or classify power quality disturbances). So, after obtaining the coefficients from the HT, the following calculations are performed: mean, standard deviation, peak value and energy. Thus, each of these statistical calculations are submitted to the inputs of the Radial Basis Function (RBF) neural network that is responsible for classifying the disturbances contained in the measured voltage signal. Despite the good results achieved by the proposed method, tests were also performed, where was replaced the HT by DWT and S-Transform. Another test was done by replacing the RBF neural network by a Multilayer Perceptron (MLP) with Backpropagation training algorithm and by a Fuzzy ARTMAP. Thus, the proposed method, which is based on HT and RBF neural network, presents better response in terms of accuracy. In Zhu, Tso & Lo (2004), a wavelet neural network was proposed for disturbances classification. However, a pre-processing step based on entropy calculation was accomplished. The results presented evidenced the potential of the proposed method for disturbances classification even under the influence of noise. Among the intelligent systems used for power quality analysis, ANN and Fuzzy Inference Systems are the most applied, as mentioned before. Intelligent systems are used because they present, as inherent characteristics, the possibility of extracting the system dynamic and being able to generalize the response provided from the system. The intelligent systems are normally applied to the pattern recognition, functional approximation and processes optimization. Taking this into account, the main purpose of this chapter is to present a collection of tools for data pre-processing including the DWT (Addison, 2002), fractal dimension calculation (Al-Akaidi, 2004), Shannon entropy (Shannon, 1948) and signal energy calculation (Hu, Zhu & Zhang, 2007). In addition to the detailed implementation of these tools, this chapter will be developed focusing on the pre-processing efficiency, considering and analyzing simulated data, when used before the intelligent system application. The results from this application show that the global performance of intelligent systems, together with the pre- processing data, was highly satisfactory concerning accuracy of response. The performance of the methodology proposed was analyzed by simulated data via ATP software (EEUG, 1987). In this case, a lot of measures were obtained by the power distribution system simulated under power quality disturbances conditions, such as: voltage sags, voltage swells, oscillatory transients and interruptions. The next step was to submit the voltage measured in the substation to the windowing. Thus, the intelligent systems have been tested on data with and without pre-processing stage. This methodology allowed to verify the improvement in power quality analysis. The results showed the efficiency of the pre-processing tools combined with the intelligent systems. Pre-Processing Tools and Intelligent Systems Applied to Power Quality Analysis 121 2. Pre-processing tools In this chapter, four main pre-processing tools will be presented, which are: Discrete Wavelet Transform, Fractal Dimension, Shannon Entropy and Signal Energy. 2.1 Discrete Wavelet Transform The Wavelet Transform (WT) has been widely used because of its most relevant features: the possibility of examining a signal simultaneously in time and frequency (Addison, 2002). Although the WT have arisen in the mid-1980s, it started to be used only by engineering in the 1990s (Addison, 2002). It is worth mentioning that the WT calculation can be performed in a continuous or discrete manner, however, in the power quality area and, more specifically in detection and classification of disturbances, it is common to use the Discrete Wavelet Transform (DWT) (Oleskovicz et. al., 2009; Moravej, Pazoki & Abdoos, 2011). The DWT can be better understood through Figure 1. Original Signal (Measured) in Time Domain Approximation Approximation Detail Detail Level 1 Level 2 Approximation Detail Level N Fig. 1. Illustrative example of decomposition performed by wavelet transform As shown in Figure 1, the WT allows the decomposition of a discrete signal in time into two levels, which are called approximation and detail. The approximations store the information concerning the low frequency components, while the details store the high frequency information. As the WT is applied to the signal, it is decomposed into other levels. Such levels are known as the leaves of the decomposition wavelet tree. From level 1, the filtered signal is decomposed into other levels from the leaf of detail, resulting in the process of downsampling by 2 (Walker, 1999), where the number of samples is reduced to half (approximation and detail of level 2) of the parent leaf (detail of level 1), as well as the frequency. This process allows us to say that with the increment of decomposition levels, the resolution in frequency increases, but the resolution in time decreases. [...]... 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Wavelet Transform and Multi-Class Relevance Vector Machines Based Recognition and Classification of Power Quality Disturbances European Transactions on Electrical Power; Vol 21, Jan 2011, pp 212222, ISSN: 15 46- 3109 Oleskovicz, M.; Coury, D V.; Delmont Filho, O.; Usida, W F.; Carneiro, A A F M & Pires, L R S (2009) Power Quality Analysis Applying a Hybrid Methodology with Wavelet Transform and Neural Networks... 200 400 60 0 1000 Windows 1200 1400 160 0 1800 2000 0.175 0.2 0.225 0.25 Fractal Dimension Calculation -1 Am plitude (V) 800 -2 -3 -4 -5 -6 0 0.025 0.05 Begin 0.075 0.1 0.125 Time (s) 0.15 Fig 11 Fractal dimension calculation applied to a voltage signal containing interruption 132 Power Quality – Monitoring, Analysis and Enhancement Amplitude (V) x 10 Oscillation 4 1 0.5 0 -0.5 -1 0 200 400 60 0 1000... 1552-1 561 , ISSN: 0378-77 96 Hu, G.; Zhu, F & Zhang, Y (2007) Power Quality Faint Disturbance Using Wavelet Packet Energy Entropy and Weighted Support Vector Machine 3rd International Conference on Natural Computation (ICNC), ISBN: 0 769 528759, Haikou, Aug 2007 Janik, P & Lobos, T (20 06) Automated Classification of Power- Quality Disturbances Using SVM and RBF Networks IEEE Transactions on Power Delivery; Vol... them been modeled for 60 0kVAr and the other for 1,200kVAr The cabling of the main feeder consists of a CA-477 MCM bare cable in a conventional overhead structure represented by coupled RL elements 130 Power Quality – Monitoring, Analysis and Enhancement As the analyzed power system has been simulated, the extraction of data is given by the ATP software at a sampling rate of 768 0 Hz In order to test... corresponds to the vector y[.] at its k-th position The DWT employed in this study was configured using a Symmlet mother-wavelet with 16 support coefficients 124 Power Quality – Monitoring, Analysis and Enhancement Signal 32 points Level 1 Approx 16 points Detail 16 points Level 2 Approx 8 points Detail 8 points Level 3 Approx 4 points Detail 4 points Level 4 Approx 2 points Detail 2 points Level... training algorithms), as well 134 Power Quality – Monitoring, Analysis and Enhancement as, the neural-genetic hybrid system use a MLP architecture with 15 neurons in the first hidden layer, 20 neurons in the second hidden layer and 1 neuron in the output layer All hidden layers use a hyperbolic tangent as activation function and the output layer uses a linear activation function 6 Conclusions This chapter . Transaction on Power Delivery 19(4), pp. 1 560 -1 568 . Methodes of Power Quality Analysis 117 Gaouda, A. M. ; Sultan, M. R. ; Chikhani, A. Y. (1999). Power Quality Detection and Classification. solution to improve the STFT analysis is described. Impulsive transients characterization is also presented. Power Quality – Monitoring, Analysis and Enhancement 1 16 8. References Amaris,. obtained amplitude, frequency and time information in order to detect, localize and classify the disturbance. Power Quality – Monitoring, Analysis and Enhancement 114 Fig.