Wavelet and S-transform Based Multilayer and Modular Neural Networks for Classification of Power Quality Disturbances

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1 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, Wavelet and S-transform Based Multilayer and Modular Neural Networks for Classification of Power Quality Disturbances C. Venkatesh, Student Member, IEEE, D.V.S.S. Siva Sarma, Senior Member, IEEE, and M. Sydulu, Member, IEEE Abstract-- This paper presents classification and characterization of typical power quality disturbances- sag, swell, interruption and harmonics employing S-transform analysis combined with modular neural network. S-transform is used to extract various features of disturbance signal as it has excellent time-frequency resolution characteristics and ability to detect disturbance correctly even in the presence of noise. Classification is performed using modular neural network with features extracted from S-transform. Modular neural network is designed by modifying the structure of traditional multilayer network into modules for each disturbance to provide less training period and better classification. Wavelet analysis is also performed and classification is performed with multilayer and modular neural networks. Simulation and experimental results show that S- transform combined with Modular neural network can effectively detect, classify and characterize the disturbances. Index Terms Voltage sag, swell, harmonics, power quality, neural networks, wavelet transform, S-transform I I. INTRODUCTION NCEASING use of power electronic switched loads, lighting controls, computer and data processing equipment, industrial plant rectifiers and inverters is resulting to poor power quality. These electronic-type loads cause quasi-static harmonic voltage distortions, inrush, pulse-type current phenomenon with excessive harmonics, and high distortion. Voltage dips and fluctuations, momentary interruptions, harmonics and oscillatory transients cause failure, or maloperation of the power service equipment. To improve power quality, it is required to detect disturbances, identify sources of power system disturbances and find solution to mitigate them. The process of automatic classification of disturbance signals are available in literature [1]-[9] to improve the speed, reliability and ease of data collection and storage. Three stages are involved in such a scheme as illustrated in Fig. 1. These are a pre-processing stage to extract the disturbance information from the generated power signal; a main- C. Venkatesh is with the Department of Electrical Engineering, National Institute of Technology (NIT), Warangal, India ( challacvs@ieee.org). D. V. S. S. Siva Sarma is with the Department of Electrical Engineering, NIT, Warangal, India ( sivasarma@ieee.org). M. Sydulu is with the Department of Electrical Engineering, NIT, Warangal, India ( sydulumaheswarapu@yahoo.co.in). processing stage to carry out pattern recognition on the disturbance data; and a post-processing stage to group the output data and form decisions on the possible nature and cause of the disturbances. Fig. 1. Block diagram of the automatic disturbance recognition system A technique capable of extracting features of all types of power quality disturbances which have different magnitude, duration and frequency spectrum is required. Multiresolution analysis using wavelet orthonormal basis decompose the signal into a set of independent frequency channels[1] having a spatial orientation tuning. Features of analysed signal are obtained by squared coefficient values[2], delta-standard deviations for various levels of wavelet coefficients[3] and energy based feature vector[4]. These features are used for classifying different power quality problems. Wavelet coefficient energies combined with fuzzy reasoning approach [5], wavelet based self-organizing learning array system[6] were attempted for automatic classification of disturbances. Other types of classification algorithm include applying genetic based optimization technique[7], randomly optimized neural network combined with discrete wavelet transform and fuzzy logic[8] and Gabor-Wigner transform[9] for detection and identification of power quality disturbances. In this paper, S-transform is used for analysis of disturbances. S-transform provides time-frequency resolution [10] while maintaining a direct relationship with Fourier spectrum. Voltage sag, swell, interruption and harmonics are the power quality disturbances considered and automatic classification of these disturbances is performed by combining S-transform with modular neural network [11], obtained by modifying the structure of multilayer neural. Simulation results show that S-transform based modular neural network has better classification accuracy than S-transform based traditional multilayer neural network. Also, it requires less number of input data compared to wavelet based neural classifier.

2 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, II. S-TRANSFORM ANALYSIS Wavelet transformation has the ability to analyse different power quality problems simultaneously in both time and frequency domains. Wavelet theory is expressed by continuous wavelet transformation (CWT) as * CWTψ x( a, b) = W ( a, b) = x( t). ψ a, b ( t). dt (1) 1/2 t b where ψ a, b ( t) = a. ψ a, a(scale) and b(translation) are real numbers. For discrete-time systems, the discretization process leads to the time discrete wavelet series as * DWTψ x( m, n) = x( t). ψ m, n ( t). dt (2) where * /2, ( ). 0 0 m m t nb a ψ m n t = ao ψ, a 0 m m a = a and b = n. b0. a0 Wavelet transform is very sensitive to noise and cannot. extract the phase information. S-transform (ST) has edge over wavelet transform that it is not affected by presence of noise in the signal [12] and it can extract amplitude and phase information of fundamental and harmonic components. ST analysis of time varying signal yields all quantifiable parameters for localization, detection and characterization of the signal [12]-[14]. ST can be seen as phase correction of wavelet transform of function x(t) in (1) with a specific mother wavelet multiplied by the phase factor j 2π ft S ( a, f ) = e. W ( a, b) (3) where the scale parameter b is the inverse of frequency f and the mother wavelet is defined as t 2 f 2 f w ( t, f ) =. e 2. e j 2π ft. (4) 2π The wavelet in (4) does not satisfy the condition of zero mean for an admissible wavelet; therefore, (3) is not strictly a CWT. Written out explicitly, ST is defined as (5). 2 2 ( a t) f f 2 j2π ft S ( a, f ) x( t).. e. e. dt 2π = (5) ST can also be written as operations on the Fourier spectrum X(f) of x(t) 2π 2α 2 2 S ( τ, f ) = X ( α f ). e f. e j2α ft +. dα, f 0. (6) The power system disturbance signal x(t) can be expressed in a discrete form as x(kt), k = 0, 1, 2,., N-1 where T is the sampling time interval and N is the total sampling number. Discrete Fourier Transform of x(kt) is obtained as 2π ft n 1 N 1 N X = x( kt ). e, (7) NT N k = 1 where n = 0, 1,., N-1. Using (6), ST of a discrete time series is given by, (let τ kt and f n / NT ) 2 2m2 j2 mk N 1 π π n m + n 2 STC kt, = X. e n. e N, n 0, (8) NT m 0 NT = where k, m = 0, 1,., N-1 and n = 0, 1,., N-1. Discrete ST can be computed quickly by taking advantage of the efficiency of FFT and convolution theorem. Sampling of S-transform is such that STC[kT,n/NT ] has a point at each time sample and at each Fourier frequency sample results in a complex valued matrix (STC-matrix). S-transform uniquely combines progressive resolution with absolutely referenced phase information. Phase information given by ST is always referenced to time t = 0. STC-matrix has each row representing particular frequency component in the signal at various sampling times. Each column represents various frequency components (magnitude and phase) in the signal at a particular time or sample. III. FEATURE EXTRACTION OF DISTURBANCE SIGNAL ST is used as a tool to extract the features of various power quality disturbances such as voltage sag, swell, interruption and harmonics. STC-matrix obtained from ST analysis of disturbance signal represented in a time-frequency plane [15] provides information of magnitude and phase of frequency content in the signal. A. Voltage Sag and Swell Fig. 2(a) shows the case for consecutive voltage sag and swells with noise signal introduced from t9 to t4. This signal contains various sag/swell magnitudes combined with normal sine wave for duration of four cycles each. Disturbances introduced at different intervals are as below: t1 to t2-30% sag t3 to t4-60% sag t5 to t6-30% swell t7 to t8-60% swell Fig. 2(b) shows the plot of fundamental rms (in per unit) of the signal versus samples obtained from STC matrix using (9) by identifying maximum amplitudes of the signal at every sample. n Af = max STC jt, NT, for n = 0, 1,., N-1. (9) This curve is called amplitude curve. Magnitudes of voltage sag identified from Fig. 2(b) are 30% (interval t1 to t2), 60.05% (interval t3 to t4), 30.02% (interval t5 to t6) and 59.98% (interval t7 to t8). These values match with the simulated values. Fig. 2(c) is the curve of normalized frequency versus magnitude of frequency components in the signal between interval t1 and t2. In this case there is only one peak occurring at fundamental frequency and its value is 0.7, indicating 30% voltage sag in the fundamental. Normalized frequency (f n ) is given by fn = h. f0 / fs, for h = 1, 2,., N/2 (10) where f o = Fundamental frequency (50Hz), f s = Sampling frequency (3.2kHz), N = Total number of samples, h = Order

3 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, of frequency. Fig. 2(d) shows level 1 detailed coefficient at every sample obtained by performing wavelet transform using db6 mother wavelet. These coefficients are high for the instants when the signal contains noise or transients, and at the instants of start and end of sag/swell in the signal. Fig. 2(d) shows that when there are transients or noise in the signal wavelet analysis fails to identify the sag at instant t3. Hence ST is having edge over the wavelet transform in detecting a disturbance under noisy condition. Fig. 2. (a). Voltage signal with consecutive sag/swell with noise, (b). Fundamental amplitude curve using ST, (c). Frequency curve using ST, and (d). Level-1 detail coefficients using wavelet transform. B. Voltage Harmonics Fig. 3(a) is a stationary signal with 1pu fundamental, (1/3)pu third harmonic and (1/5)pu fifth harmonic components. Fig. 3(b) shows the amplitude (rms value) of the fundamental component of the signal obtained from ST analysis. Fig. 3. ST analysis of harmonic signal, (a). Voltage signal with 50Hz, 150Hz and 250Hz frequency components, (b). Fundamental amplitude curve, (c). Frequency curve, and (d). Phase-frequency curve Fig. 3(c) is the normalized frequency curve shows peak values of 1pu, 0.333pu and pu at dominant frequencies of fundamental, third and fifth order harmonics, respectively. X and Y values here indicate the normalized frequency and rms value (in pu). Phase angles of all the frequency contents extracted from STC matrix are calculated using (11) and normalized frequency versus phase angle is drawn as shown in Fig. 3(d). Im [, / ] tan 1 ag STC jt n NT Re al STC [ jt, n / NT ], for n = 1, 2,., N/2. (11) X and Y coordinates in Fig. 3(d) are the normalized frequency and phase angles, respectively at corresponding frequency. Harmonic magnitudes and phase information in the signal are correctly extracted by ST analysis. C. Features used for Classification Amplitude and frequency curves obtained from STC-matrix are used to extract the features of power quality disturbances. In this paper, four features are used by calculating standard deviation and mean of amplitude and frequency curves as specified below: Index1 Standard deviation of amplitude curve Index2 Mean of amplitude curve Index3 Standard deviation of frequency curve Index4 Mean of frequency curve. (12) D. Features used for Characterization Once the disturbance is detected, quantification of disturbance is performed. Voltage sag, swell and interruption are characterized with their magnitude of disturbance. Remaining voltage available during disturbance is evaluated from fundamental amplitude curve and calculating the minimum value of matrix A f from (9). Percentage of voltage sag, swell or interruption represents drop in rms magnitude in signal from nominal value (1 pu) given by ( Af ) % Dm = 1 min 100. (13) In case of harmonic signal number of peaks and peak values are evaluated from frequency curve of the signal. IV. MODULAR NEURAL NETWORK Features obtained from S-transform analysis are used as input data for classification using artificial neural network. S- transform based feedforward network[17], probabilistic network[18] used for classification have large training time. To reduce training time and to improve the accuracy of neural network in classifying power quality disturbances, the complex task is divided into subtasks to obtain modular neural network. Modular neural network (MNN) consists of more than one neural network, called as modules, to handle each subtask. Each module is independent, domain specific and respond to a particular set of data input it is intended for [13]. Solution of the overall task is achieved by combining the result of each module. Structure of MNN is shown in Fig. 4. MNN process has been widely used in applications such as to discriminate the direction of faults for transmission line protection [19], for pattern recognition [20], condition monitoring of industrial machines [21]. Advantage of modular structure is that individual model responds to a given input faster than a complex monolithic system. Such a modular structure can be imbibed in different types of network, including the multilayered neural network (MLNN). In this paper, an approach of modular neural network is explored to classify

4 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, Fig. 4. Model of modular NN technique. power quality disturbance signals. Simulation results are presented and performances of S-transform based MNN and MLNN are compared in the next section. V. CLASSIFIER PERFORMANCE AND SIMULATION RESULTS Disturbances such as sag, swell and interruption are generated by MATLAB program with different percentages, durations and instants of disturbances. Patterns of harmonics are generated with random selection of harmonics for various percentages of harmonic as compared to fundamental component. Here V m is taken as 230 volts, fundamental frequency ω = 2π f 1 where f 1 = 50Hz and T = 1/ f 1. Totally a set of 652 patterns are generated with 200 patterns of sag, swell and harmonics each, 50 patterns of interruption and 1 pure sine wave. In this work 6.4 khz sampling frequency (128samples/cycle) is selected. Training of neural network is performed with a data set of 491 patterns consisting of 150 patterns of sag, swell and harmonics disturbances, 40 patterns of interruption and 1 pattern of pure sine wave signal. Remaining data set of 160 disturbance patterns and 1 pattern of the normal sine wave are used for testing. ST analysis is performed for all power quality signals generated and index1 to index 4 given in (12) are calculated. Total size of training data set is with 4 index values for 491 training patterns. Features of disturbance data set are not completely separable and hence neural network based classification is used. Flowchart in Fig. 5 shows the steps for classification of simulated disturbance signals. Database of features obtained from S-transform is generated. For classification both MLNN and MNN are used. If the classified disturbance is sag/swell/interruption, magnitude of the disturbance is calculated from the fundamental amplitude curve. For the signal classified as harmonic signal, number of peaks occurring in the frequency curve is found. These represent the dominant harmonics and their magnitude and phase of harmonic components are calculated. Multi-layer neural network structure shown in Fig. 6 with three layers input, hidden and output layers is implemented. The input layer has 4 nodes represented by features extracted by ST; hidden layer has 8 nodes, while output layer has 5 nodes representing normal sine wave and 4 classes of disturbances: voltage sag, voltage swell, interruption and harmonic distortion. This structure is called ST-MLNN. Fig. 5. Flowchart of ST based NN Classification Fig. 6. ST based multilayer neural network (ST-MLNN) structure used for power quality classification. TABLE I PERCENTAGE CLASSIFICATION ACCURACY OF ST-MLNN Signal Classification result Test Sine Set Sag Swell Interruption Harmonics wave Sine wave Sag Swell Interruption Harmonics Classification accuracy: 95.03% Simulation results with ST-MLNN for classification of power quality problems are given in Table I. In case of sag classification, out of 50 patterns, 1 pattern is misclassified as interruption resulting to 98% accuracy of sag classification. The overall accuracy of ST-MLNN is calculated by taking average of diagonal elements of Table I and it is found to be 95.03%. The model presented is capable of classifying the dataset but the classification accuracy is less. In this paper this problem is overcome by designing modular neural network structure.

5 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, A. Implementation of MNN Improvement in training time and classification accuracy is obtained by modifying the structure of MLNN to implement MNN with five modules for classification of pure sine wave and four disturbances as shown in Fig. 7. This structure is called ST-MNN - has 4 input nodes, 8 hidden nodes and 1 output node in each module. Hence each module is a multilayer network. Training of ST-MNN is performed by applying training data set simultaneously to all the 5 modules. Desired output of the module corresponding to disturbance input is set to 1 and outputs of all other modules are set to 0 during training. Outputs of all the modules are then combined by maximum operation. The largest of all output nodes is considered as the output of ST-MNN and determines the class of disturbance voltage (pure sine, sag, swell, interruption or harmonics). individual disturbance classification and hence in overall performance as compared to ST-MLNN. This is due to the fact that MNN has modules consisting of individual neural network for each disturbance. The training time of modular neural network is reduced as each module is trained for its corresponding disturbance class. The testing time of MNN and MLNN is same as the input is applied simultaneously to all the modules where the input is processed in parallel. B. Performance Comparison Wavelet transform is applied to same disturbance signals with daubachies6 mother wavelet and multiresolution technique upto level 7 Delta standard deviations are considered as features and are calculated for signal database using (5). Classification with wavelet based classifier using multilayer (WT-MLNN) and modular (WT-MNN) networks is performed with 7 input nodes corresponding to 7 delta standard deviations. Classification accuracy of these classifiers is shown in Table III. Fig. 8 shows comparison of ST-MNN performance with other classifiers. ST-MNN has better classification accuracy for individual disturbances and hence improvement in overall accuracy. TABLE III COMPARISON OF ST AND WAVELET BASED POWER QUALITY DISTURBANCE CLASSIFICATION Signal Test Set WT- WT- MLNN MNN Sine wave Sag Swell Interruption Harmonics Classification accuracy % 94.41% Fig. 8. Classification accuracy of ST-MNN compared to other classifiers Fig. 7. Structure of S-transform based modular neural network (ST-MNN) for power quality classification. TABLE II PERCENTAGE CLASSIFICATION ACCURACY OF ST-MNN Signal Classification result Test Sine Harmonic Set Sag Swell Interruption wave s Sine wave Sag Swell Interruption Harmonics Classification accuracy: 98.14% ST-MNN classification results are given in Table II. The performance accuracy is 98.14%. Test results with ST-MNN has shown improvement in the classification accuracy for VI. EXPERIMENTAL VERIFICATION In the previous sections it is shown that ST could identify the disturbance correctly in the presence of noise and also that ST could identify the harmonics. In this section, STC matrix construction is performed for load voltage of a practical system. Experimental setup consists of 750 kms artificial transmission line model with 12 pi-sections supplied from 3- phase, 400 volts, 50 Hz supply connected to five resistive loads of 2A, 500W each at the receiving end as shown in Fig. 9. Receiving end voltage (load voltage) is kept constant at 110 volts rms during the experimentation. Experimentation is performed for various sag/swell conditions by sudden increase/decrease in the load. Interruption in the voltage is introduced by opening the mains switch (CB1). Load voltage

6 16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, signal is stored in a Tektronix make TDS 3032B, 300 MHz digital oscilloscope. performed with modular neural network. Modular neural network has given better classification accuracy and reduced training time by using less number of hidden layer nodes compared to S-transform based traditional multilayer neural network. Simulation and experimental results verify that S- transform based modular neural network has correctly classified and characterized the disturbances. Fig. 9. Block diagram of transmission model with loads. Fig. 10. Swell caused due to sudden removal of load. Figs. 10(a) shows R-phase load voltage waveform stored in oscilloscope for swell introduced by sudden removal of load. Voltages recorded during experiment are 110 volts and 122 volts respectively. The sampling frequency of the oscilloscope is 10 khz with 200 samples per cycle. Fig. 10(b) and Fig. 10(c) shows fundamental amplitude plot and frequency plot obtained from ST. Voltage magnitudes obtained from ST are volts and volts for normal and swell conditions indicating 10.85% swell. These values are comparable with measured values. Many cases of voltage sag, swell and interruption are considered and disturbances were correctly classified and ST results are matching with measured values. Fig. 10(d) gives the level-1 detailed coefficients obtained from wavelet transform analysis. Wavelet transform is affected by presence of measurement noise and fails in this case to identify occurrence of swell. Hence, ST is suitable for classification and detection of power quality disturbances even with noise present in the signal. VII. CONCLUSIONS S-transform is used in this paper to extract the features of disturbance signals and is found to detect disturbance correctly even in the presence of noise. 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