Rule-Based Expert System for PQ Disburbances Classification Using S-Transform and Support Vector Machines

Transcription

1 International Review on Modelling and Simulations (I.RE.MO.S.), Vol. 4, N. 6 December 2011 Rule-Based Expert System for PQ Disburbances Classification Using S-Transform and Support Vector Machines M. A. Hannan 1, Tea Chiang Wei 2, Alex Wenda 3 Abstract This paper presents a rule-based expert system for automatic identification and classification of PQ disturbances by combining the improved S-transform and SVM. The combined tools are used to integrate the computation process and extracted features to formulate rules for classification of the PQ disturbances.rule formulataion is developed by comparing standard deviation value of a disturbance signal that is obtained from the S-transform analysis. SVM technique is used for data classification and regression for training and testing the class level and control feature parameters, respectively.thus, based on the distinctive features through SVM, the S-Transform formulated appropriate rules and features contour that can easily be classify the PQ disturbances. Copyright 2011 Praise Worthy Prize S.r.l. - All rights reserved. Keywords: Rule-Based Expert System, PQ Disturbances, Classification, S-Transform, SVM F F 1,,F 5 X i X 1 THD,, σ f(x) g(x) x i y b N s Φ Nomenclature Feature indices 1 st, 2 nd, 3 rd, 4 th and 5 th feature indices Standard deviation Clean signal S-transform absolute value Frequency of the largest amplitude Voltage component Harmonic order The fundamental frequency Total harmonic distortion Time-frequency representation S-transform transforms time series Gaussian modulation function Gaussian width Optimal decision function Decision boundary hyper lane Training sample Expected classification error Label of category Lagrangian multiplier Bias vector Number of support vectors Slack variable Non linear transform Penalty factor Kernelfunction Radial base function parameter Loss function Linear combination of image vector Number of support vectors I. Introduction The power quality (PQ) disturbances such as sags, wells, harmonics, notches, transients, interruptions, flickers, etc are become major issues for electric utilities and its customers. [1]-[2]. These types of disturbances are often caused by faults, dynamic opeartions, solidstate switching or nonlinear loads of the system [3]-[4]. Poor electric quality can result in malfunctioning of power electronic devices, process controller, motors, frequency converters, current-source inverters and so many industrial equipments [5]-[7]. Thus, in the deregulated market, the PQ monitoring would be an effective means for providing better customer services, improve the quality of power supply as well as reinforcing competitiveness among the utilities [8]. In recent years, many research has been carried out on developing tools and methodologies for PQ disturbnaces detection and classification, monitoring as well as improving the quality of electric power systems [8], [9]. Several methodologies such as artificial neural network [10], probabilistic neural network [9],[11], expert system [12], fuzzy logic [13], nearest neighbor rule [14], and so on many have been discussed in order to identify and classify the types of PQ disturbances. To monitor power quality disturbances, short time discrete Fourier transform (STFT) is most often used [15]. However, for non-stationary signals, the STFT does not track the signal dynamics properly due to the limitations of a fixed window [16]. Also, STFT cannot be used to analyze transient signals comprising both high and low frequency components [17]. On the other hand, wavelet transform is the notable tool for detection, localization and classification of the disturbances [18]. Manuscript received and revised November 2011, accepted December 2011 Copyright 2011 Praise Worthy Prize S.r.l. - All rights reserved 3004

2 However, the noises lower down the performance of wavelet as the spectrum of noises overlaps with that of power quality disturbances [9]. S-Transform is an approach attracts the researchers for the detection and classification of PQ disturbances. Due to its good time-frequency characteristic, it is very suitable for PQ disturbances analysis as well [9]. S- Transform avoids the requirement of testing various families of wavelets to identify the best one for the accurate classification. Further, the decomposition of the disturbance signals at different resolution levels is not required, thereby reducing the memory size and computational overhead [19]. Probabilistic neural network (PNN) was trained with an orthogonal least-square algorithm featured from S- Transform for recognization the wavelet and its effective classification [11], [20]. Featured based different types of PQ disturbances are analyzed and tested using S- Transform decision tree. However, S-Transform capabilities are often significantly degraded in real practice under noisy environment [21]. Gaing has classified different types PQ disturbances using wavelets and PNN [15], where decomposition levels of wavelet and time duration of each disturbance are taken as features and applied to PNN for classification. However, a large number of features may result in high memory and computational overhead [8]. Haibo et al. [18] has presented the classification of PQ disturbances using a self learning array of wavelet transform at different features and decompodsition levels to identify the best one for a better classification. A drawback of these approaches are that it fails to detect disturbances that appear periodically and in many cases, the effect of electrical noise is not adequately considered in these investigations. [22]. The Support Vector Machine (SVM) is a new universal learning machine introduced in the structural risk minimization to discriminate PQ disturbance patterns [23]-[24]. Accordingly, Vivek et al. (2006) prooposed an approach which uses S-Transform to extract distinct features of typical power quality disturbances and SVM to perform the data mining task and effective PQ disturbances calssification based on ANN demonstration [3]. However, the speed of convergence and the accuracy are affected by the signal to noise ratio in the ANN schemes [8],[25]. From the extensive analyses which already proved that the extracted features using the S-transform analysis exhibit distinctive features for different types of PQ disturbances. So that, based on these distinctive features, derivation of appropriate rules can be done to classify the PQ disturbances. This paper deals with a rule-based expert system for automatic identification and classification of PQ disturbances by combining the S- transform and SVM. This combined tools are used to integrate the computation process and extracted features to formulate rules for classification of the PQ disturbances. Power quality problems Literature review Power quality events Characterization power systemelectroma gnetic phenomena Fig. 1. Framework for intelligent PQ disturbances classification II. PQ data collection PQ meter II Off-line data On-line data Sampling design PQ disturbances classification Display feature value Display Y test value Display decision Loading data and plotting graph Methodological Framework The methodological framework of an intelligent classification of PQ disturbances includes detailed statement of the PQ problems, PQ data collection, feature extraction and support vector machines as shown in Fig. 1. The electromagnetic phenomena of power quality events are charactersied from the existing published review [2],[7],[20],[22]-[27] to develop a new intelligent classification system. The most important part of this framework was on-line PQ data collection using PQ meter II. The off-line data were collected from Malaysian utilities in order verifies the on-line PQ disturbances classification. The sampling design was performed for keeping the data in time order and to provide information to a specific character. Feature extraction transforms raw data or pattern from its original form to a new form for intelligent classification such a way that the distorted signal data was mapped into S-transform domain. The features would be extracted from S-transform analysis in term of time frequency representation (TFR) curve. The contour of the TFR curve would formulated the rules for the operation of SVM algorithm. A new SVM algorithm is developed splited into classification module and regression module, dealing with high-dimensional input features for classification of an optimal decision function and characterise maximum margin algorithm of linear and non-linear function, respectively. Then, after loading testing data, SVM classification and regression algorithm provides rule based decision of feature values and Y test values for accurate PQ disturbances classification. III. Features Extraction Feature vector extraction S-Transform domain TFR curve Rules formulation Support vector machine SVM algorithm SVM classification module SVM regression module Feature extrcation is a processing operation that transforms raw data or initial measurement pattern to a 3005

3 new pattern feature. In the proposed method, the transformation of distorted signal data is mapped into S- transform domain, which provides patterns that closely resemble the non-stationary disturbances. The feature extraction includes TFR curves, feature indices, rules and S-tranform theory. III.1. TFR Curve A time frequency representation (TFR) curve represents the energy distribution of different frequency bands over a certain period of time. The TFR curve is linear over a pure sinusoid, which value is considered as a reference. All signals are normalized to per unit value to avoid the feature components with large dynamic range dominating small feature components. The features of TFR curve contour is extracted from the S-transform analysis. This extracted features are used to formulate rules for classifying the PQ disturbances comparing the TFR value of a signal and the TFR value of a pure sinusoid. III.2. Feature Indices Features indices such F 1, F 2, F 3, F 4 and F 5 are derived and defined from the S-transform analysis to formulate the rules for classifying the various PQ disturbances: i) F 1 is the first feature considered the amplitude factor as follow: 1 (1) where d s1 and d s2 are the maximum and minimum values of standard deviations of a distorted signal, respectively. The p s1 and p s2 are the maximum and minimum values of a clean signal, respectively. ii) The second feature, F 2 is given by: iii) The third feature, F 3 is given by: (2) (3) where s 2 is the S-transform absolute value of a distorted signal iv) The fourth feature denoted by F 4 is the S-transform absolute value of the frequency of the largest amplitude, fm at each time step which is given by: (4) v) The fifth feature, F 5 is THD calculated from the FFT algorithm. The feature is given by: (5) where X is the voltage component, i is the harmonic order, X 1 is the fundamental frequency and THD is the total harmonic distortion. III.3. Rules The different values of standard deviation (STD) obtained from the S-transform analysis are used to formulate a rule by comparing STD value of a disturbance signal with STD value of a clean signal. The rules are in the form of IF-THEN logic. IF statement is the classification function linked to the features characteristic of various PQ disturbances. THEN part is linked to a particular PQ disturbance which is matched with the IF statement. Accordingly, six rules have been formed for the purpose of PQ disturbance classification: i) Rule 1: IF 0.991<F 1 <1.01 and IF <F 2 <0.001 and IF <F 3 < and IF 0.50<F 4 <0.55 and IF 0.008<F 5 <0.025, THEN the signal is clean. ii) Rule 2: IF <F 1 <0.994 and IF <F 2 <0.0 and IF <F 3 < and IF 0.457<F 4 <0.53 and IF 0.0<F 5 <0.35, THEN the disturbance is voltage sag. iii) Rule 3: IF 0.997<F 1 <1.020 and IF 0.0<F 2 <0.02 and IF <F 3 < and IF 0.477<F 4 <0.73 and IF 0.075<F 5 <0.30, THEN the disturbance is a voltage swell. iv) Rule 4: IF 0.957<F 1 <0.973 and IF <F 3 < and IF 0.225<F4<0.50 and IF 0.3<F5<3.5, THEN the disturbance is an interruption. v) Rule. 5: IF 0.994<F 1 < and IF <F 2 < and IF <F 3 < and IF 0.485<F 4 <0.53 and IF <F 5 <0.20, THEN the disturbance is a notching. vi) Rule 6: IF 0.997<F 1 < and IF <F 2 <0.021 and IF <F 3 < and IF 0.49<F 4 <0.53 and IF 0.015<F 5 <0.075, THEN the disturbance is impulsive transient. III.4. S-Transform Theory The S-transform transform a time series, h(t) to a time-frequency representation, S(τ, f) to localizes the real and imaginary spectra. Gaussian modulated cosinusoids is basic function for the S-transform. The S-transform of a time series h(t) is defined as:,, where G(τ, f ) is the Gaussian modulation function, f is the frequency, t and τ are both time, respectively. The Gaussian modulation function G(τ, f ) is defined as: (6) 3006

4 , 2 (7) where σ is the gaussian width, which is defined as: 1 Substituting (7) and (8) into (6), the final S-transform equation becomes:, 2 IV. Support Vector Machines (8) (9) SVM is a classifier of supervised learning algorithms to identify the decision boundary between different classes. The learning strategy is based on the principle of structural risk minimization. SVM is comprehended into two specified training samples of two different categories by constructing an optimal separate hyper plane to guarantee maximum distance between each training sample and hyper plane. In this paper, SVM technique is used for data classification and regression for training and testing the class level and control feature parameters, respectively. IV.1. SVM Classification SVM algorithm used for classification is to construct an optimal decision function, f(x) that accurately predicts unseen data into two classes and minimizes the classification error: (10) where g(x) is the decision boundary hyper lane and is derived from a set of training samples as follows:,,,, (11) where each training sample x i has M features and R is the expected classification error. Again, a set of label samples is expressed as follows:,,,, 1, 1 (12) where y is the label of category. The general expression of the linear discrimination of decision boundary hyperplane in d-dimention space is:, (13) where,, in which arethe Lagrangian multiplier used for converting mentioned problem into quadratic programming problem and optimal hyper lane can also be solved. The sample x i is known as support vector (SVs) appearing in the separate interval planes and y i are the label of categories. The bias vector b, the classify function in (10) is defined as follows:, (14) In case of linearly separable data, all SVs lied on the margin and hence the number of all SVs can be very small. Accordingly, the decision boundary hyper lane g(x) is determined by only using a subset of the training samples and the rest of the training samples are not needed:, (15) where x is the input test vector, (x, x i ) is the inner product, N s is the number of support vectors, and b is the bias term. In the case where a linear decision boundary is inappropriate the SVM can map the input vector, x, to a higher dimensional feature space. If the data are not linearly separable in the input space, the object function is turned as follows:, 1 2 (16) where is the slack variable and C is the penalty factor. Simultaneously, through a non-linear transform the input space is maped into a higher dimensional space named feature spaced in which optimal hyper lane can be solved. Again, the inner product calculation is turned into a kernelfunction K at condition,,. Thus, final classification function of (14) and decision boundary function of (15) can be written as follows:,, (17), (18) In brief, the proposed procedure in using SVM is shown as below: i) Transform data to the format of an SVM software. ii) Conduct simple scaling on the data. iii) Consider the radial base function (RBF) kernel K(x;y) = iv) Use cross-validation to find the best parameter C and iv) Use the best parameter C and to train the whole training set 3007

5 v) Test In this paper, RBF is chosen in relation between class labels and nonlinear features. The RBF kernel can nonlinearly maps samples into a higher dimensional space. Furthermore, the linear kernel is a special case of RBF with a penalty parameter and some parameters (C, ). The second reason is that the polynomial kernel has more hyperparameters than the RBF kernel, on the other hand, the RBF kernel has less numerical difficulties. Accordingly, the extracted features (F1, F2, F3, F4, F5) of power quality data from S-tranform technique is used as features in identification and classification of power disturbances such as, voltage sag, voltage swell, notching, and impulsive transient. The support vector regression is used the epsilon intensive loss function to ensure existence of the global minimum and at the same time optimization of reliable generalization bound. Fig. 4 shows details of epsilon band with slack variables and selected data points slack variables, where x is the input support vector, ω is the object function, b is biaas term and epsilon ε is loss of function. IV.2. SVM Regression SVM also can be applied for regression other than classification, containing features that characterize maximum margin algorithm to find and optimize the generalization bounds. The bounds are lied on the loss function to ignore errors and situated within the certain diatance of the true value, which is known as epsilon intensive loss function. Fig. 2 and Fig. 3 shows an example of one dimensional linear and non-linear regression function with epsilon intesive band, where the cost of the errors on the training points are measured by the variables. Fig. 4. Details of epsilon band with slack variables, selected data points and its slack variable In SVM regression, the input support vector x is first mapped onto an m-dimensional feature space by using some fixed non-linear mapping and then a linear model is constructed as follows:, (19) where, 1,, denotes a set of nonlinear transformations. Again, SVM regression measured the quality of estimation by -insensitive loss function as follows:,, 0,, (20) Fig. 2. One-dimensional linear regression with epsilon intensive band SVM performs linear regression in the high-dimension feature space using -insensitive loss to reduce model complexity by minimizing. Thus, SVM regression is formulated the minimization of the following function as follows: 1 2 (21) where the slack variables,, 1, to measure the deviation of training samples outside -insensitive zone. Thus, the optimization problem can transformed into the dual problem and its solution is given by:, 0,0 (22) Fig. 3. One-dimensional linear regression with epsilon intensive band where is the number of support vectors and K is the kernel parameter. A good setting of meta-parameters parameters C, and the kernel parameters give good SVM generalization performance (estimation accuracy). 3008

6 Parameter C determines the trade off between the model complexity and the degree to which deviations larger than are tolerated in optimization formulation. For example, if C is too large, then the objective is minimizing without the model complexity part in the optimization formulation. Parameter controls the width of the -insensitive zone and used to fit the training data. The value of can affect the number of support vectors used to construct the regression function. Thus, both C and -values affect model complexity. Thus, SVM regression is applied to avoid difficulties of using linear functions in the high dimensional feature space and transform optimization problem into dual convex quadratic programmes. The loss function is applied to penalize errors that are grater than threshold - in regression case. The sparse representation of the decision rule is usually led by loss function to give significant algorithmic and representational advantages. representation curve which is in the form of contour. The S-transform clearly shows that the existence of voltage sag duration by the sudden changes in the time frequency contours. The resolutions of the contours also shows the reduction during the events. It can also be observed that at fault condition the time frequency representation is non-linear, however, when there is no fault, the the time frequency curve is linear. This combination of the feature shows a unique ability to classify the disturbance region. The intelligent system send the data to classification module and then return back in the GUI as a graph for input signal, time-frequency representation curve from the S-transform analysis. Thus, provide automatic disturbance classification result. V. Results and Discussion This section discuss about all the findings from the development of S-Transform and SVM classification of power quality disturbances. The features of the power quality disturbances is mapped S-Transform domain using FFT and provides decision of the classification. The power quality disturbances signals are analyzed for testing the performance of the classification by rule-based feature values. We have used F1, F2, F3, F4, and F5 features of power quality disturbances, which are used as input signal in the SVM classification module. The classification module obtained the feature values by S- Transform analysis and compared with the rules, accordingly provides decision of the power quality disturbance classification. For example, Table I shows the F1, F2, F3, F4, and F5 features values which are lies in formulated classification rule 2 and provide decison as voltage sag. The discrete S-Transform of the PQ signal generates time-frequency, time-amplitude and amplitudefrequency contours, which are recognized the type of disturbance visually. TABLE I FEATURES VALUES IN FORMULATING CLASSIFICATION RULE 2 Feature Classified PQ Features Classification rule 2 values events F i) <F 1 <0.994 F ii) <F 2 <0.0 F iii) <F 3 < F iv) 0.457<F 4 <0.53 F v) 0.0<F 5 <0.35 Classified as sag Figs. 5 show the input signal of voltage sag and the time frequency contour of the voltage sag in which the feature extraction process is done by mapping the data of a distorted signal into its S-transform domain. Then, the features of the disturbance signals are extracted from S- transform analysis in terms of time-frequency (a) (b) Figs. 5. Mapping distorted signal into S-transform domain as a) input signal of voltage sag b) time frequency contour of the voltage sag Table II shows the F1, F2, F3, F4, and F5 features values which are lies in formulated classification rule 3 and provide decison as voltage swell. The training data F1, F2, F3, F4, and F5 features of the power quality disturbances insert to the SVM classification algorithm for training purpose, which inform the SVM classification type of PQ disturbances decision. The features are extraction by using S-transform and FFT. The performance of the classification is higher, which depends on the training data i.e. with the increased training data, the precision of SVM classification is increasing. TABLE II FEATURES VALUES IN FORMULATING CLASSIFICATION RULE 3 Feature Classified Features Classification rule 3 values PQ event F i) 0.997<F 1 <1.020 F ii) 0.0<F 2 <0.02 F iii) <F 3 < F iv) 0.477<F 4 <0.73 F v) 0.075<F 5 <0.30 Classified as swell Figs. 6 show the input signal of voltage swell and the 3009

7 time frequency contour of the voltage sag. It is seen that during the voltage swell, the time frequency contour increased to show the existence of the event. Otherwise the time frequency curve is linear. (a) (a) (b) Figs. 7. Mapping distorted signal into S-transform domain as a) input signal of voltage interruption b) time frequency contour of the voltage interruption (b) Figs. 6. Mapping distorted signal into S-transform domain as a) input signal of voltage swell b) time frequency contour of the voltage swell Table III shows the F1, F2, F3, F4, and F5 features values which are lies in formulated classification rule 4 and classified the PQ event as interruption. The training data F1, F2, F3, F4, and F5 features of the interruption signal loaded into the SVM classification module to provide the classification decision as interruption. Thus, user can observe the decision in the SVM model GUI. TABLE III FEATURES VALUES IN FORMULATING CLASSIFICATION RULE 4 Classified Features Feature values Classification rule 4 PQ event F i) 0.957<F 1 <0.973 F ii) <F 2 <0.02 F iii) <F 3 < F iv) 0.225<F4<0.50 F v) 0.3<F5<3.5 Classified as interruption Fig. 7(a) shows the corresponding waveform of the input interruption signal. The S-transform generates time frequency contours, which displays the disturbance patterns for visual identification for power quality disturbances. The contours provide excellent features, which can be used by a pattern recognition system for classifying the power quality disturbances. Fig. 7(b) shows the time frequency contours of the interruption signal. It can be seen that the S-Transform clearly showed the existence of interruption signal by the sudden changes in the time frequency contours. The resolutions of the contours showed the abrupt reduction of contours during the interruption period and become linear at no interruption condition. Similarly, the training data of F1, F2, F3, F4, and F5 features, can classify the power quality disturbances like transients, notching, harmonics etc using S-Transform formulated rules and FFT through the SVM classification algorithm. Again, the mapping data of a distorted signal extracted from S-Transform provides the time frequency contour curve to detect the power quality disturbances. Generally, the time-frequency contour value of a pure sinusoid is compared with the time-frequency value of a distored contour to represent the specific energy distribution at different frequency bands over a certain period of time. The extensive analysis of the findings proved that the extracted features using the S-transform analysis and FFT exhibit distinctive features for different types of PQ disturbances through SVM algorithm. Thus, based on these distinctive features, the S-Transform formulated appropriate rules and features contour can easily be classify the PQ disturbances. VI. Conclusion This paper proposed an automatic method for identification and classification of PQ disturbances by using the improved S-transform and SVM. The timefrequency contours of the input voltage disturbances provide excellent features, which can be used by a pattern recognition system for classifying the power quality disturbances. This combination of the feature shows a unique ability to integrate the computational process and extracted features to formulate the rules for PQ disturbance classification. The precision of SVM classification is increased by increaseing the training data. The results shows that integrated method is a strong tool to ditinguish PQ disturbances with high reliability and precision. Thus, the proposed S-transform and SVM 3010

8 method is better than that of fuzzy logic, PNN and STFT, respectitively. References [1] IEEE Std , IEEE Recommended Practice for Monitoring Electric Power Quality, IEEE Inc., New York, pp. 1-59, [2] M A Hannan, Azah Mohamed. PSCAD/EMTDC Simulation of Unified Series-Shunt Compensator for Power Quality Improvement, IEEE Transaction on Power Delivery, vol. 20, no. 2, pp , April [3] K. Vivek, M. Gopa, B.K. Panigrahi, "Knowledge Discovery in Power Quality Data Using Support Vector Machine and S- Transform," Third International Conference on Information Technology: New Generations (ITNG'06) ITNG, pp , [4] M A Hannan and K W Chan, Modern Power Systems Transients Studies Using Dynamic Phasor Models, The proceeding of the International Conference on Power System Technology - POWERCON, pp. 1-5, November [5] M. M. Morcos, J. C. Gomez, Flicker Sources and MitigationIEEE Power Engineering Review, pp 5-10, [6] Zhang, M., Xu, W., Nassif, A. 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Mojdehi, Influencing Zero Sequence Current in Order to Improve Power Quality Disturbances, International Review of Electrical Engineering (IREE), vol. 5, no. 2, pp , March [27] M. Eslami, H. Shareef, A. Mohamed, Application of PSS and FACTS Devices for Intensification of Power System Stability, International Review of Electrical Engineering (IREE), vol. 5, no. 2, pp , March Authors information 1,2,3 Dept. of Electrical, Electronic & Systems Engineering UniversitiKebangsaan Malaysia, Bangi, Selangor, Malaysia. *Corresponding author hannan@eng.ukm.my M. A. Hannan received the B.Sc. degree in electrical and electronic engineering from Chittagong University of Engineering and Technology; M. Sc. and Ph.D in Electrical, Electronic & Systems Engineering from UniversitiKebangsaan Malaysia in 2003 and 2007, respectively. He is an associate professor in the dept. of Electrical, Electronic & Systems Engineering. His research interests are in inverter controller, FACTS & custom power devices and artificial intelligence. Tea Chiang Wei is a graduate student the Dept. of Electrical, Electronic & Systems Engineering, Faculty of Engineering and Built Environment, UniversitiKebangsaan Malaysia.His research interests are in power quality and artificial intelligence in power system. Alex Wenda is a Ph D scholar the Dept.ofElectrical, Electronic & Systems Engineering, Faculty of Engineering and Built Environment, UniversitiKebangsaan Malaysia. His research interests are in power quality, intelligent system and artificial intelligence in power system. 3011