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Abstract— The objective of this paper is to detect the Power Quality Events (PQEs) by Wavelet Transform (WT) and classification by Weighted Extreme Learning Machine (WELM). Power Quality Events are non-stationary in nature and Discrete Wavelet Transform (DWT) is used to analyze those signal by Multi Resolution Analysis (MRA). In this approach, the distinctive features of PQ event signals have been acquired by applying the WT on all the spectral components and in order to analyze the performance of the proposed method on noisy conditions, three types of PQ event data sets are constructed by accumulating noise of 25, 35 and 45dB. Weighted ELM is an efficient learning algorithm for generalized single hidden layer feedforward networks (SLFNs), which is implemented to recognizing the various PQEs classes. Based on very high performance under ideal and noisy conditions, the proposed WT-WELM method has robust recognition structure that can be used in real power systems.

Index Terms— Disturbance Shannon Entropy Index, Wavelet Transform (WT), Weighted Extreme Learning Machine (WELM), Nonstationary power signal

I. INTRODUCTION

OWER quality is the set of parameter elucidating the properties of power supplied to consumer under normal

operating condition in terms of characteristics of voltage or current (magnitude, frequency, phase, etc.), with poor quality, power electrical device may swerve from its proper operation or may fail permanently [1]. So the recent concern over the quality of electrical power is being aggravated by the client and end user, ultimately this concern made researchers for carrying out research work in this area. Basically the process of improving PQEs quality undergoes three steps: preprocessing, feature extraction and categorization.

P

For feature extraction number of methods are adopted by researchers till date which were a fiasco later on when unable to assuage the necessary requirements. Fast Fourier transform is a suitable signal processing tool for periodic and stationary signal only, so for analyzing PQEs which are nonstationary and non-periodic in nature, there are a number of methods are

adopted but wavelet transform (WT) take the race due to localize in nature in both time and frequency domain. Due to its multi resolution capability, it's able to overcome the demerit of short time Fourier transom (STFT) by introducing variable window [2]. Due to variable size window it can extract low frequency component at the high frequency area and high frequency component of low frequency area. It is the most exact way representation of signal than STFT by preserving global energy and reconstructing exact feature. Basically wavelet transform which generate numerous bases from a given orthogonal wavelet function are indexed by three naturally interpreted parameter called position, scale and frequency. so we can say wavelet decomposition is the most flexible tool dealing with different type of transient signal. so here author likely to prefer WT as the time-frequency signal analysis tool for feature extraction.

Number of methods proposed for recognition and classification of PQEs like Artificial Neural Network (ANN), Support Vector Machine (SVM), Fuzzy Logic (FL), Genetic Algorithm (GA) etc. Though ANN has high accuracy for real time application and easy computational capability but its convergence speed and accuracy depends on architecture of the network and noise in signals. SVM also has potential to handle large features, high learning process but failed to handle its advantages in case of minimum sample. Genetic Algorithm can accurately classify PQEs generated due to the dynamic performance of the power system and damp sub-harmonic signals, but require large time for computation. By analyzing the merits and demerits of all the proposed method a new classifier is adopted here called Extreme Learning Machine (ELM). ELM is a linear single layer feed forward network, which exhibit high computational time, high learning accuracy, less complexity in architecture.

In this paper author have proposed WT with Weighted Extreme Learning Machine (WELM) for detection and classification of various PQ events at various noise levels. Recently ELM has emerged as a new effective classificationtool for training single layer feed forward neural network(SLFNN) more efficiently [3]. Less computer time, suitable feature extraction, the ability to operate at noise prone

Mrutyunjaya Sahani is with the Institute of Technical Education and Research, Siksha ‘O’Anusandhan University, Bhubaneswar 751030, India (e-mail: [email protected]).

Siddharth Mishra is with the EEE department, Institute of Technical Education and Research, Siksha ‘O’Anusandhan University, Bhubaneswar 751030, Odisha, India (e-mail: [email protected]).

Ananya Ipsita is with the EIE department, Institute of Technical Education and Research, Siksha ‘O’ Anusandhan University, Bhubaneswar 751030, Odisha, India (e-mail: [email protected]).

BinayakUpadhyay is with the EEE department, Institute of Technical Education and Research, Siksha ‘O’ Anusandhan University, Bhubaneswar 751030, Odisha, India (e-mail: [email protected]).

Detection and Classification of Power Quality Event using Wavelet Transform and Weighted

Extreme Learning MachineMrutyunjaya Sahani, Siddharth Mishra, Ananya Ipsita, Binayak Upadhyay

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signal, more efficiently than other traditional classification methods make it trend of the recent era.The organization of this paper is as follows, Section II focuses on the WT. Section III describes the feature extraction of PQEs. In Section IV, we present the ELM approach for pattern recognition. The Section V accumulates the experimental verification followed by the conclusion.

II.WAVELET TRANSFORM

In 1982 Jean Morlet, a French geophysicist, introduced the concept of a wavelet [4]. The wavelet means a small wave which decays fast after an oscillation. The WT decomposes the signal into different scales at various levels of resolution. Now a day’s wavelet transform can be considered as the most dominated signal processing tool applicable to various power system applications like detection, feature extraction, de-noising technique, power system protection etc. due to its such friendly properties like multi resolution analysis, local analysis and perfect reconstruction [5].Equivalent mathematical conditions for wavelet are:

∫−∞

∞

|ψ (t )|2 dt<∞ (1)

∫−∞

∞

|ψ (t )| dt=0 (2)

Morlet first considered wavelets as a family of functions constructed from translations and dilations of a single function called the "mother wavelet" ψ(t). The mother wavelet can be any finite energy function like Haar, Morlet, Coefliet, Simlet and Daubechies which are chosen carefully according to the properties we required and they are defined by

ψa,b( t )= 1√|a|

ψ ( t−ba ) , a,b ∈ R, a ≠0

(3)The parameter a is the scaling parameter or scale, and it

measures the degree of compression. The parameter b is the translation parameter which determines the time location of the wavelet. If |a| < 1, [6] then the wavelet in above equation is the compressed version (smaller support in time domain) of the mother wavelet and corresponds mainly to higher frequencies. On the other hand, when |a| > 1, then ψa, b(t) has a larger time-width than ψ (t) and corresponds to lower frequencies. Thus, wavelets have time-widths adapted to their frequencies. This is the main reason for the success of the Morlet wavelets in signal processing and time-frequency signal analysis.

A. Discrete Wavelet TransformThe discrete wavelet transform is an implementation of

continuous wavelet transform using discrete set of wavelet scales. This transform decomposes the signal into mutually orthogonal set of wavelets, which differentiated it from CWT. Discrete wavelet transform took the place of CWT working on its disadvantages like heavy computational load, difficulties in implementation and redundancy problem. In DWT the

frequency information has different resolution at every scale which is not seen in CWT. The DWT can be expressed as

DWT (a,b )=∑ f( t ) ψa,b( t ) (4)where a and b vary discretely in real space. Functions are

wavelets and it is clear from above equation that the DWT depends on two parameters (a and b) which represent the scale and translation factors of the wavelet. By this transform, f is decomposed into the superimposed wavelet yielding a set of DWT coefficients that characterize f.

B. Multiresolution AnalysisIn discrete wavelet transform case we use a multiresolution analysis technique (MRA) for analyzing signal at different frequencies with varying resolution [7]. This approach applicable while dealing with high frequency components for short duration and low frequency component for long durationAccording to the highest frequency component present in the signal, the cutoff frequency of the filters is chosen for analysis. Resolution reveals the probability of information occurrence which changes by filtering process and scale can be changed by down sampling or up sampling process. Here we have down sampled the filter output by 2 Decimated by a factor of 2 means making the sample number half. DWT can decompose the input signal into smaller frequency range time domain components of smaller frequency bands because of these disturbances in signal can be split into smaller components which is easier to analyze.

Fig 1. Decomposition of Original Signal

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III. FEATURE EXTRACTION

The classifier input signal is a preprocessing signal. The time domain PQEs is converted to the wavelet domain before applying as input to the extreme learning machine. Feature extraction is the key for recognition of particular patterns of PQEs even the best classifier will perform poorly if the feature selection is not correct. The wavelet coefficients obtained by wavelet and multiresolution analysis (WMRA) to PQEs have the meaningful information, but it is impractical to apply the classifier input due to large data size. The suitable distinct features must be extracted from those coefficients to minimize the dimension of the feature vectors and to recognize the PQEs effectively. The disturbance Shannon entropy index based feature extraction method in this study is described below. In this paper, the detail and approximation coefficients are obtained by applying 10 level WMRA to the PQEs. The Shannon entropy at each decomposition level of purity (E j , E j+1 ) and disturbance (

~E j ,~E j+1 ) signal is calculated by

using the following equation

E j=-D j2 ln D j

2 , j=1,2,⋯,10 (5)

E j+1=-A j2 ln A j

2 (6)

~E j=−~D j2 ln {~D j

2 , j=1,2,⋯,10 ¿ (7)~E j+1=−~A j

2 ln {~A j2¿ (8)

Stipulated 0 ln 0=0 .

Where D j and

A j are the detail and approximate coefficient of WARA signals. j is the decomposition level and N is the number of coefficients of detail and approximation at each decomposition level. The disturbance Shannon entropy index is calculated from the pure and disturbance signals is given below.

ΔE j=E j−~E j (9)

ΔE j+1=E j+1−~E j+1

(10)The resultant feature vector can be represented mathematically asΔE=[ ΔE1 ,ΔE2 ,⋯, ΔE10 , ΔE11 ] The obtained feature vector is passed to the classification stage. The MATLAB (Wavelet toolbox) software [8] was used to calculate the wavelet decomposition. The disturbance energy index ΔE for fourteen classes of disturbances analyzed with the db4 wavelet filter for 10 levels are shown in Fig. x. The variations in the disturbance energy index of wavelet detailed and approximation coefficients for disturbances is used by the extreme learning machine for the PQEs classification.

Fig 2. Variation in the disturbance Shannon entropy index for different PQ disturbances

In our study, we have considered fourteen different types of PQEs and TABLE I provides the definition of different power signal disturbance patterns and their parametric variation which was used to create the training and validation set. The distinctive disturbances energy index features belonging to each class signal have been extracted by applying WT on the PQEs data and a total of 11 features have been applied to the ELM classifier as input. The PQEs data in this study consist of real, synthetic and synthetic data with noise. Synthetic data have been obtained with different parameter in MATLAB environment with the sampling frequency of 3.2 kHz. The method is not only classifying the PQEs efficiently but also have detection capability. It has been shown in the Fig. 2 for the occurrence of voltage sag with transient, multiple spike and notch signal

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Fig 3(a) Occurrence of voltage sag with transient, multiple spike and notch signal. (b) Output of wavelet transform.

IV. ELM

Feed forward neural networks are optimal classifiers for nonlinear mappings that employ a gradient descent method for weight and bias optimization. The main factors that affect the performance of a traditional neural learning algorithm include:i. A small value of learning parameter causes the learning

algorithm to converge slowly, whereas a higher value load to instability and divergence to local minima.

ii. Gradient descent based learning is an extremely time consuming process for many applications.To improve the inherent slow learning ability of

traditional optimization methods, Huang et al. [9] Proposed ELM to train a single layer feed forward neural network (SLFNN).

Fig 4 Single-hidden layer feedforward network

Apart from other learning algorithms, ELM randomly assigns weight and biases to generate the hidden nodes, subsequently the system can be serve as a linear network and the output weights can be enumerated empirically.

Consider N training samples (xi, ti) with L hidden nodes, the mathematical model of the SLFNs is

∑i=1

L

β i gi( x j)=∑i=1

L

β iGi (wi ,b i ,x j )=t j , j=1 ,. . .. ,N . (11)

The above N equation can be written compactly as:

H∗β=T (12)

Where H is the hidden layer output matrix, is the output weight and T is the target vector.

H=[ h( x1)⋮

h( xN )]N×L

=[ G(w1 ,b1 ,x1 ) ⋯ G(wL ,bL ,x1)⋮ ⋯ ⋮

G(w1 ,b1 ,xN ) ⋯ G( wL ,bL,x N ) ]N×L

;

β=[β1T

⋮β L

T ]L×m

and T=[t1T

⋮t L

T ]N×m

The least square solution with minimal norm is analytically empirically resolute using Moore-Penrose “generalize” inverse H† [10, 11]:

When N<L: β=H∗T = HT ( Iλ

+HHT )−1T (13 )

When N>L: β=H∗T = ( Iλ

+HT H )−1 H T T (14 )

As can be seen from the two formulas above, a positive small value I/λ is added to the diagonal of H*HT or HT*H in the calculation of output weights or better performance.

Given a new sample x, the output function of the ELM

classifier is obtained from f ( x )=sign h (x )β

f ( x )N ×N=sign h( x ) HT ( Iλ

+HHT )−1 T (15)

f ( x )L×L=sign h( x ) ( Iλ

+H T H )−1 HT T (16 )

A. Weight Calculation

The weight matrix to train Ns no of signals, W= diag{Wii}, i=

1, 2… N generates automatically from the energy feature

vector of each classes from the Wavelet array of original

signal.

Weighted Scheme = {Wii = Wii /mean(Energy)}

Finally, to recognize each PQEs accurately, a constant pattern

W is calculated for each individual class and equation (13) is

modified based on it as follows:

When N<L: β=H∗T = HT ( Iλ

+H*W*HT )-1 T*W (17 )

When N>L: β=H∗T = ( Iλ

+HT *W*H )-1 HT *W*T (18)

TABLE IDifferent Mapping Function and its Expression

Kernel function Expression

Tan hyperbolic G( w,b,x )= tan( w . x+b )

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Sigmoid G( w,b,x )= 11+ exp( -w .x+b )

Sinusoid G( w,b,x)=sin(w . x+b)

Hard limit G( w,b,x )=¿ {1 if w . x+b ≥0 ¿ ¿¿¿Triangular basis G( w,b,x)=¿ {1 -abs( w .x+b ) if -1≤w . x+b ≤1 ¿¿¿¿

Radial basis G( w,b,x )=exp(−(w . x+b )2)

On the other hand, it is not essential that the feature mapping function h(x) is always known. The most prominent kernel in use is Gaussian Kernel but the proposed ELM used tan hyperbolic Kernel function which also provides a unified solution for the “generalized” SLFNs.

V. RESULT AND DISCUSSION

HHT in combination with ELM empowers to be an efficient technique for PQEs recognition. In our study, we have considered ten different types of PQEs and are given here,

TABLE II

PERFERMANCE COMPARISION ON CLASSIFICATION ACCURACY USING W-ELM

PQE signals Hidden NodeType

Wavelet Function

Haar Db12 Db4 Sym8 Sym12 Bior3.7 Bior5.5 Coif5

Ideal Case

Tan hyperbolic 72.60 94.00 97.00 90.9 91.00 87.60 91.4 97.6Sinusoid 79.00 97.10 99.10 99.4 81.2 79.40 99.1 99.2Sigmoid 79.40 88.30 79.4 84.40 88.6 90.40 86.60 90.30

Triangular basis 82.70 80.00 98.7 74.90 76.30 79.40 80.10 86.60Radial basis 79.3 84.90 78.2 80.40 87.00 88.90 79.10 82.10

45 dB



35 dB



25 dB



Note. The best classification accuracy is distinguished by bold and shading.

1) CL1-Mumentary Interruption;2) CL2-Sag;3) CL3-Swell;4) CL4-Harmonics;5) CL5-Flicker;6) CL6-Notch;7) CL7-Spike;8) CL8-Transient;9) CL9-Sag with harmonics;

For each of the above PQEs 100 cases are considered. Out of these, 50 cases are taken for training the ELM classifier and 50 cases are taken for testing.The overall efficiency of the classifier is computed using the formula given as in (19)

Overall efficiency =Number of PQEs classified accuratelyTotal nunber of PQEs

(19)

Table I represent the recognition efficiency of the

WT_WELM method for ideal and noisy environment. This table depicts a comparison between different kernel and wavelet combination. It has been found that Tan Hyperbolic kernel in addition to Db4 wavelet gives best accuracy in all condition. The performance accuracies of the proposed method are compared with other classifiers in Table-III.

TABLE IIICOMPARISION OF THE PROPOSED METHOD TO EXISTING

METHODSMethod Classification

AccuracyWavelet transforms with neural network [12] 94.37

S-Transform with probabilistic neural network [13] 95.55Wavelet transforms with neural fuzzy [14] 96.5

IMF-H with probabilistic neural network [15] 97.22Wavelet packet and support vector machine [16] 97.25

Fast Dyadic S-Transform with CFDT [17] 98.66DWT with ELM (proposed) 99.10

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The compared existing classifiers can detect and recognize only single PQEs, whereas the proposed technique has the capability to detect multiple concurrent PQEs in a very short time with reduced complexity. The high learning speedSuperior classification accuracy in both noiseless and noisy environment of the proposed methodology effectively.

VI. CONCLUSION

A novel electrical power supply signal decomposition, feature extraction and classification algorithm have been introduced in this paper. The proposed WT-WELM is a promising method

for better classification speed and recognition accuracy than the other methods for classifying multiple simultaneous PQEs patterns. The simulation results indicate that the method is competent and can classify single as well as multiple concurrent events accurately in the presence of noise. The less computational time, suitable feature extraction, better overall efficiency at various noise levels and the relatively simple but powerful architecture are the major features of the proposed WT-WELM technique. The comparison of classification accuracies concludes that the proposed method is a robust method for the detection and classification of PQEs

REFERENCES

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[16] W. Tong, X. Song, J. Lin, and Z. Zhao, “Detection and classification of power quality disturbances based on wavelet packet decomposition and support vector machines,” in Proc. ISCP, vol. 4, pp. 1–4,2006.

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