Classification of Power Quality Disturbances Using S-Transform Based Artificial Neural Networks

Suriya Kaewarsa Department of Electrical Engineering, Faculty of Industry and Technology

Rajamangala University of Technology Isan, Sakon Nakhon Campus Sakon Nakhon, Thailand

e-mail: suriya_ka@hotmail.com

Abstract—This paper presents a method based on S-transform and artificial neural network for detection and classification of power quality disturbances. The input features of the neural network are extracted using S-transform. The features obtained from the S-transform are distinct, understandable and immune to noise. These features after normalization are given to a feed forward neural network trained by the back propagation algorithm. The data required to develop the network are generated by simulating various faults in a test system. The proposed method requires less number of features and less memory space without losing its original property. The simulation results show that the proposed method is effective and can classify the power quality signals even under noisy environment.

Keywords- power quality disturbance; S-transform; artificial neural network; wavelet transform

I. INTRODUCTION Power qual i ty has become an important issue for

electric utilities and its customers. As a result, power quality study is gaining interest. Degradation in quality of electric power is normally caused by power-line disturbances such as voltage sag/swell with and without harmonics, momentary interruption, harmonic distortion, flicker, notch, spike and transients, causing problems such as malfunctions, instabilities, short lifetime, failure of electrical equipments and so on. In an electric distribution network faults may cause voltage sag or momentary interruption whereas switching off large load or energization of a large capacitor bank may lead to voltage swell. On the other hand, use of solid- state switching devices and nonlinear and power electronically switched loads such as rectifiers or inverters may cause harmonic distortion and notching in the voltage and current. Use of arc furnaces may lead to flickers and transformer energization, or capacitor switching may cause transients and lightning strikes

may lead to spikes. To monitor power quality disturbances, short time discrete Fourier transform (STFT) is most often used. But for non- stationary signals, the STFT does not track the signal dynamics properly due to the limitations of a fixed window width chosen a priori [1,2]. Thus, STFT cannot be used successfully to analyze transient signals comprising both high and low frequency components.

On the other hand, wavelet transform uses short windows at high frequencies and long windows at low frequencies; thus closely monitoring the characteristics of non-stationary signals. These characteristics of the wavelet transform provide an automated detection, localization, and classification of power quality disturbance waveforms [3,4].

Although wavelet transform has the capability to extract features from the signal in both time and frequency domain simultaneously and has been applied in the detection and classification of power quality, it exhibits some disadvantages [5] like excessive computation, sensitivity to noise level and the dependency of its accuracy on the chosen basis wavelet.

S-transform (ST) is method for the feature extraction. It is an extension to the ideas of wavelet transform and is based on a moving and scalable localizing window and has characteristics superior to other transforms. S-transform can be seen as the “phase correction” of continuous wavelet transform. This transform has the ability to detect the disturbance correctly in the presence of noise [6].

The other advantage of S-transform over wavelet transform is that it avoids the requirement of testing various families of wavelets to as identify the best one for the accurate classification. Further, the decomposition of the disturbance signals at different resolution levels is not required in the S-transform, thereby reducing the memory size and computational overhead [7].

This paper presents a method based on S-transform and artificial neural network for classification of power quality

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disturbances. S-transform is mainly used to extract features of power quality events and artificial neural networks are mainly used to construct a multiclass classifier which can classify power quality disturbances according to the extracted features.

II. S-TRANSFORM S-transform (ST) can be seen as the “phase correction”

of continuous wavelet transform (CWT). The CWT of a function h(t) is defined as

W( ,d) h(t)w(d, t )dt.�

��� � ��� (1)

The scale parameter determines the “width” of the wavelet w(d, t) and thus controls the resolution. The ST of a function is defined as the CWT with a specific mother wavelet multiplied by the phase factor

j2 ftS( , f ) e w(d, )�� � � (2) where the mother wavelet is defined as

t2f 2 j2 ftw(t, f ) | f | / 2 e e .� �� � (3)

The scale parameter d is the inverse of the frequency f. The wavelet (3) does not satisfy the condition of zero mean for an admissible wavelet. Therefore (2) is not strictly a CWT. Written out explicitly, the ST is defined as

(r t)2f 2 / 2 2 ftS( , f ) 1/ 2 h(t) | f | e e dt.�

� � � �

��� � � � (4)

The ST can also be written on the Fourier spectrum H(f ) of h(t)

2 2 2/ f 2 2S( , f ) 1/ 2 H( f )e e d .�

� � � � ���

��� � � � �� (5)

By taking advantage of the efficiency of the FFT and the convolution theorem, the discrete ST can be computed quickly. The ST localizes the phase spectrum as well as the amplitude spectrum. The S- transform performs multi resolution analysis on a time varying signal as its window width varies inversely with frequency. This gives high time resolution at high frequency and high frequency resolution at low time. Since power quality disturbances make the power signal a non stationary one, S-transform can be applied effectively .

In this paper, the ST amplitude matrix is used to analyze the power disturbances in which the rows are the frequencies and the columns are the time values. Each row displays the ST amplitude with all frequencies at the same time and each column displays the ST amplitude with time varying from 0 to N-1 in the same frequency, where n= 0,1,……N/2 -1. The features necessary for

power quality disturbances classification are extracted from the S-matrix. Further, from the S-matrix important information in terms of amplitude, frequency and phase are extracted. Standard statistical techniques are applied to extract the features. Many features such as amplitude, slope of the amplitude, time of occurrence, mean, standard deviation and energy of the transformed signal are widely used for classification [7, 8]. In this paper, the following features are considered.

Feature 1, the energy of the signal x(n) is given

by �2E abs x(n)� where abs represents absolute value. Feature 2, the mean of the signal x(n) is mean(x). Feature 3, the peak value is max(x) and feature 4, standard deviation which is the square root of variance.

III. ARTIFICIAL NEURAL NETWORK The artificial neural network for the power quality disturbance classification problem consists of three layers with one hidden layer. The input layer has number of features obtained from the S-transform of the signal. The networks are trained with the training data set using back propagation algorithm. The hidden layer neurons have tangent hyperbolic function as the activation function and the output neurons have linear activation function. Trial and error procedure [9] is followed to select the suitable number of neurons in the hidden layer. The neural network architecture in this class shares a common feature that all neurons in a layer are connected to all neurons in adjacent layers through unidirectional branches. The branches have associated weights that can be adjusted according to the learning rule

ij ijw kdE / dw .� � � (6)

Where k is a constant of proportionality, E is the error function and ijw represents the weights of the connection between neuron i and neuron j. The weight adjustment process is repeated until the difference between the node output and the actual output are within some acceptable tolerance. Feed forward neural network training is usually carried out using the back propagation algorithm. The standard back propagation algorithm [10] for training the network is based on the minimization of the energy function representing the instantaneous error. The energy function is defined as

�p 2

q qq 1

1E(m) d y .2 �

� �� (7)

Where qd represents the desired network output for

the thq input pattern and qy is the actual output of the network. Training the network with back propagation algorithm results in a non-linear mapping between the

Feature Extraction using S-Transform

Power quality disturbances

Data classification using ANN

Type of PQ disturbances

input and the output variables. The generalization capability of the neural network is analyzed by using a standard method in statistics called independent validation. The method involves dividing the available data in to training set and test set. The entire data is usually randomized first. The training data is next split in to two partitions: first partition is used to update the weights in the network and the second partition is used to assess the training performance periodically to the over training problem [11]. The data set are then used to assess how well the network has generalized.

IV. P ROPOSED METHOD The proposed methodology for disturbance waveform classification is based on artificial neural network (ANN). Neural network approach for any application involves two stages: network development and actual usage of the network. The various stages involved in the network development are data generation, feature extraction, data normalization and network training. Generation of the appropriate training data is an important step in the development of ANN models. A large number of training data is generated through off-line simulation process. Seven type of power quality disturbances namely normal, sag, swell, harmonics, transients, outage and voltage fluctuation are generated. The signal under noisy environment is generated by adding uniformly distributed gaussian noise of 30 dB with the original signal. The features of the input data are extracted by finding the S-transform of the signal and by applying standard statistical techniques to the transformed signal. During training of the neural network, higher valued input values may tend to suppress the influence of smaller ones. Also, if a raw data is directly applied to the network, there is a risk of the simulated neurons reaching the saturated conditions. If the neurons get saturated, then the changes in the input value will produce a very small change in the output value. This affects the network training to a greater extent. To avoid this, the raw data is normalized before the actual application to the neural network. One way to normalize the data x is by using the expression :

minn

max min

(x x ).(Rank)x Starting value.(x x )�

� �

(8)

Where nx is the normalized value and maxx and minx are the minimum and maximum values of x . The features after normalization are presented to the neural network and is trained using the back propagation algorithm. After training, the network is tested with the test data to assess the generalization ability of the network. The network is also tested with signals under noisy environment.

V. SIMULATION RESULTS This section presents the details of the ANN- based

model developed for disturbance waveform classification. The power quality disturbances such as sag, swell, transients, harmonics, outage and voltage fluctuation were generated by creating various faults like single line

Figure 1. Proposed method for classification process.

to ground faults, double line to ground fault, 3-phase short circuit fault and harmonic injection. Training samples were obtained from different locations in an attempt to collect samples from different locations. Totally, 3500 samples were generated with 500 samples from each category. The signals were sampled at 256 points/cycle and the normal frequency is 50Hz. The S-transform was applied to the signals to extract the relevant features. The features considered here are energy, standard deviation, mean and variance. Based on the feature extraction by the S-transform method, four dimensional feature set for training and testing are constructed. The dimensions here describe the different features derived from the S-transform. The extracted features were given to the ANN and the network was trained using back propagation neural network. After training, the network was tested with the test data. The performance of the network during training and testing are given in the table I.

TABLE I. ANN RESULTS USING S-TRANSFORM AND WAVELET TRANSFORM

Type Training error

Testing error

Time (s)

Number of epochs

Accuracy (%)

Wavelet Transform

0.003 0.0193 1007 2500 98.94

S-Transform

0.009 0.0276 1022 2500 97.43

For comparison, wavelet transform was applied to extract the features and the extracted features are used to train the network. In wavelet based ANN, multiresolution analysis technique is used in which the signal is decomposed into 8 levels. The same features used in S-transform is considered here .i.e, energy, mean, standard deviation and peak value. The feature vector size is 32 (8 x 4), where 8 represents 8 levels. The classification results during training and testing are shown in the table I. From the table it is clear that the wavelet based ANN gives best performance than the S-transform method. Similarly, the overall accuracy for the wavelet based classification is 98.94 % which is higher than that of the S-transform. The details of correctly classified events and the misclassified events using wavelet transform and S-transform are displayed in table II and table III, respectively. The diagonal elements represents correctly classified power quality events. The off-diagonal elements represent the misclassification. Seven types of power disturbances are taken and are as follows: normal (C1), sag (C2), swell (C3), harmonics (C4), transients (C5), outage (C6) and voltage fluctuation (C7).

TABLE II. CLASSIFICATION RESULTS OF WAVELET TRANSFORM BASED ANN

Type C1 C2 C3 C4 C5 C6 C7 C1 500 0 0 0 0 0 0

C2 0 500 0 0 0 0 0 C3 1 0 496 2 0 1 0

C4 0 4 0 490 6 0 0

C5 1 0 2 0 497 0 0

C6 0 10 0 5 0 485 0

C7 1 4 0 0 0 0 495 Overall accuracy = 98.94 %

TABLE III. CLASSIFICATION RESULTS OF S-TRANSFORM BASED ANN

Type C1 C2 C3 C4 C5 C6 C7 C1 500 0 0 0 0 0 0

C2 0 480 5 4 1 10 0

C3 0 0 500 0 0 0 0

C4 0 15 2 475 3 5 0

C5 0 0 10 0 480 10 0 C6 0 5 10 0 0 485 0

C7 0 5 0 0 5 0 490 Overall accuracy = 97.43 %

In an electrical power distribution network, the practical data consist of noise. Therefore, the proposed approach has to be analyzed under noisy environment. The gaussian noise is widely considered in the research of power quality issues. We have obtained the noise signals for all the 7 classes with SNR = 30 dB and operated with S-transform and wavelet transform for feature extraction. Then, with these features, ANN is trained and

subsequently tested for automatic classification. Then the performance of the network using the above transforms are compared in the noisy environment. From the tables IV to VI, it is seen that, the S-transform based ANN classifier gives best performance than the wavelet based method. Similarly, using S-transform, the over all accuracy is 98.48 % where as using wavelet transform, the accuracy is 84 %. Thus it is clear that, the S-transform based ANN classifier can effectively classify the different kinds of power quality disturbances in the noisy environment.

TABLE IV. ANN RESULTS USING S-TRANSFORM AND WAVELET TRANSFORM

Type Training error

Testing error

Time (s)

Number of epochs

Accuracy (%)

Wavelet Transform

0.0443 0.0566 1002 2500 84.00

S-Transform

0.0100 0.0315 854 2500 98.48

TABLE V. CLASSIFICATION RESULTS OF WAVELET TRANSFORM BASED ANN

Type C1 C2 C3 C4 C5 C6 C7 C1 500 0 0 0 0 0 0 C2 25 400 0 50 25 0 0

C3 0 0 420 10 0 70 0

C4 50 0 20 400 30 0 0

C5 0 60 20 0 390 0 30

C6 20 0 70 0 30 380 0

C7 10 0 10 30 0 0 450 Overall accuracy = 84.00 %

TABLE VI. CLASSIFICATION RESULTS OF S-TRANSFORM BASED ANN

Type C1 C2 C3 C4 C5 C6 C7 C1 500 0 0 0 0 0 0

C2 3 494 0 0 0 3 0

C3 0 0 500 0 0 0 0

C4 0 4 0 490 6 0 0 C5 2 0 10 0 488 0 0

C6 0 10 0 5 0 485 0

C7 1 4 5 0 0 0 490 Overall accuracy = 98.48 %

VI. CONCLUSIONS This paper proposed a method for classification of power quality disturbances by using S-transform based artificial neural network. In this paper, an attempt has been made to extract efficient features of the power quality disturbances using S-transform. The features extracted from the S-transform are very simple and yet very effective. The classification accuracy of the network is very high, even in the presence of noise. The network is quick to train to give 98.48 % classification accuracy. This is quiet significant as the classification accuracy of the wavelet

multiresolution analysis combined with neural network is of the order of 84 %. Compared to the wavelet transform, S-transform can be quickly calculated, so that the proposed method is efficient. Moreover, this method shows good scalability and low sensitivity to noise levels.

ACKNOWLEDGMENT The author gratefully acknowledge the financial support

from Rajamangala University of Technology Isan, Sakon Nakhon Campus, during a period of this work.

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