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A Generalized Empirical Wavelet Transform for
Classification of Power Quality Disturbances
Karthik Thirumala, Student Member, IEEE, Amod C. Umarikar and Trapti Jain, Senior Member, IEEE
Discipline of Electrical Engineering Indian Institute of Technology Indore Indore, India Email: {phd1301102004, umarikar, traptij}@iiti.ac.in
Abstract—This paper proposes a generalized empirical wavelet transform (GEWT) for the recognition of single and combined power quality (PQ) disturbances. The FFT based frequency estimation is adaptive, requires no prior information and is also capable to diagnose all the PQ disturbances. The im- proved spectral segmentation followed by an adaptive filter design accurately extracts the fundamental frequency component, thereby enabling the extraction of informative features. Thus, the proposed approach combines the GEWT and a simple rule based decision tree (DT) for accurate recognition of most significant PQ disturbances. The DT classifier with five features extracted from the GEWT is refined and finally tested on 1200 simulated as well as three real disturbance signals. The proposed scheme is found to be computationally efficient and performs satisfactorily with a good classification accuracy. Index Terms—Generalized Empirical Wavelet Transform (GEWT), Decision Tree, Power Quality (PQ), PQ Disturbances.
I. INTRODUCTION
Quality of electric power is usually deteriorated due to the occurrence of disturbances such as voltage sag, swell, interrup- tion, transients, harmonics and flicker [1]. These disturbances result in mal-operation of circuit breaker, failure of end-user equipment and degrade the performance of transmission sys- tem equipment. Identification of the disturbances and its source is preliminary to deploy a mitigation device for improving the PQ. Most of the traditional power analyzers do not provide sufficient temporal information of the disturbances. Hence, the monitoring equipment should be capable to recognize and classify the PQ disturbances [2]. The signal processing techniques frequently employed for feature extraction include fast Fourier transform (FFT), Wavelet transform (WT), S-transform (ST), empirical mode decomposition (EMD) and Kalman filter [3]–[6]. The features are then utilized as input to a classifier such as expert system, rule base, fuzzy logic (FL), artificial neural network (ANN) and support vector machine (SVM) [7]–[11]. Various approaches have been proposed with different combinations of signal processing techniques and classifiers to enhance the accuracy of classification [12]. The approximation coefficients of the WT are not unique and contain information of a band of frequencies including the fundamental frequency. Similarly, the ST and EMD suffer from mode mixing and the features extracted from these components may not reflect the disturbances acceptably. It can also be inferred that for
an accurate recognition of disturbances, signal decomposition with predefined filters necessities unique novel features or a complex classifier. Nevertheless, a linear classifier with basic features is adequate to identify the significant PQ disturbances if the filtering approach is adaptive and accurate. The rule based decision tree (DT) classifier requires less computational resources and is flexible. The empirical wavelet transform (EWT) proposed in [13] decomposes a non-stationary signal by designing a bank of filters according to the frequency information. However, it requires prior information of number of frequencies present in the signal which is impractical for continuous monitoring. This has been overcome in [14], where a EWT based approach, proposed for PQ application, uses minimum magnitude (dM ) and minimum frequency separation threshold (dF ) for esti- mation of actual frequencies. However, the fixed frequency threshold is not suitable to analyze all sorts of PQ signals and may result in inaccurate extraction of fundamental frequency component in case of disturbances. Therefore, this paper pro- poses a generalized EWT (GEWT) with an adaptive frequency threshold for an improved spectral segmentation. The paper aims to recognize the significant PQ disturbances with a simple DT by using features extracted from the GEWT. The developed GEWT first computes the dF threshold re- quired for the FFT based frequency estimation. This novel dF , is estimated adaptively to separate the fundamental fre- quency components from its neighbouring frequencies. The information about the existence of frequencies in vicinity of fundamental is obtained by a primary investigation of the signal amplitude variation, as explained in section II. The improved spectral segmentation followed by adaptive filtering extracts the frequency components with minimal overlapping; thereby the features can represent the disturbances. The major contributions of this paper are new GEWT algorithm for fast and accurate decomposition of disturbance signals and an efficient, simple DT classifier to identify them. II. PROPOSED METHODOLOGY A. Generalized Empirical Wavelet Transform The EWT approach proposed in [14] decomposes the signal into its individual components perfectly but may result in indefinite components in case of disturbance signals. This is the consequence of fixing the minimum frequency separation
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Fig. 1. Voltage sag signal and its fundamental.
threshold in prior for estimation of frequencies from the Fourier spectrum. Actually, the peaks in the Fourier spectrum near fundamental frequency don’t correspond always to the actual existence of low frequencies. It may also be spectral leakage of the fundamental component due to the drastic change in either amplitude or fundamental frequency. Thus, fixing the frequency threshold may either over estimate few fake low frequency interharmonics or may under estimate the frequencies. As a result, the fundamental component extracted may not reflect the actual change in amplitude due to overlap with interharmonics or imperfect reconstruction. This has been overcome in this paper, by considering an adaptive frequency threshold that varies according to the frequencies present near the fundamental frequency. The presence of low frequency interharmonics can be investigated from the time domain signal rms variation as well rather than relying only on the frequency domain information. Thus, the signal rms variation confirms the existence of low frequency components and can be related to the new frequency threshold. The number of variations (N V ) of signal rms and the new frequency threshold (dF ) is obtained from the following steps. The signal RMS of the nth cycle is defined as
xrms(n) =
S
∑^ nS
(n−1)S+
x(i)^2 (1)
Where n=1,2,.. 10 represents the order number of signal cycles, S is the number of samples in one cycle and x(i) is the sampled signal. The rms vector xrms having values calculated for all ten cycles is
xrms = [xrms(1), ..., xrms(n), ..., xrms(10)] (2)
The variation of the power signal is obtained from the rms vector [3] as
SV = xrms − mean(xrms) (3)
Fig. 2. Voltage fluctuation signal and its fundamental.
Then, the number of signal variations, N V representing the presence of low-frequency interharmonics is the total number of zero crossings of the signal variation vector, SV. The N V < 3 indicates that no interharmonics exist near the fundamental frequency component and hence the new frequency threshold dF is chosen as 25 Hz to extract the fundamental component accurately. Else if N V ≥ 3 , it is confirmed that low-frequency interharmonics are present in the signal and the amplitude variation will have a pattern. An extensive study has been done to investigate this pattern and relate to the frequencies present. The study revealed that a signal containing interharmonics in the range of 25 to 75 Hz with a frequency of fi Hz will have the amplitude variation at a frequency of | 50 − fi| Hz. Consequently, the number of zero crossings N V of the signal variation SV can be related to the new frequency threshold dF as
dF = (quot(N V, 2) + rem(N V, 2) − 1) fres (4) Where, quot(N V, 2) is the quotient of N V and 2 and rem(N V, 2) is the remainder of N V and 2. fres is the frequency resolution based on the duration of time window. In this work, fres is taken as 5 Hz. The complete procedure of the generalized empirical wavelet transform is listed as follows.
- First compute rms of the signal for each cycle and assess the new frequency threshold, dF based on (N V ).
- Estimate frequencies f = {fi}i=1, 2 ..,N from the Fourier spectrum, X(ω) using the magnitude and frequency threshold dF.
- Compute boundaries Ωi for segmentation of the Fourier spectrum i.e., [0, Ω 1 ], [Ω 1 , Ω 2 ], ..., [ΩN − 1 , f 2 s ].
- Based on the boundaries computed, design a low pass φi(ω) and N-1 bandpass filters Ψi(ω) in the frequency domain using the empirical wavelets defined in [13].
- Finally, obtain the individual mono-frequency compo- nents by the inverse FFT of the filtered coefficients [13].
Fig. 4. Scatter plot of PQ disturbances in feature space.
Thus, mean of the HHD of ten cycles is considered as the last feature
F 5 = HHDm = mean(HHD) (12)
C. Decision Tree
A decision tree (DT) is initially formed with well known set of rules considering the standards and practical signal characteristics. Thereafter, the DT has been refined based on the exhaustive analysis of 100 signals belonging to each class, totally 1200 signals representing 11 PQ disturbances. Fig. 3 shows the optimal DT constructed for evaluation based on the features extracted. The classes are labeled as C0 - normal signal, C1 - voltage interruption, C2 - voltage sag, C3 - swell, C4 - harmonics, C5 - flicker, C6 - oscillatory transients, C7 - notch, C8 - spike, C9 - sag with harmonics, C10 - swell with harmonics and C11 - flicker with harmonics.
III. RESULTS AND DISCUSSIONS To evaluate the performance of the proposed approach, sig- nals covering all extreme intensities with varying fundamental frequency (49.5-50.5 Hz) and different phase angles have been considered for verification. Moreover, all the signals generated contain differing noise levels with SNR ranging from 25 dB to 55 dB. Total of 2400 signals corresponding to normal and 11 PQ disturbances (100 signals for each class) are generated in MATLAB [6] at a sampling rate of 10 kHz. The signals are normalized to 1 p.u., and length of the windowed signal is chosen as 200 ms. Finally, the optimal DT classifier is verified by testing the 1200 simulated and three real disturbance signals. The real harmonics with interharmonics and transient signals are obtained with a voltage probe and OROS-34 data acquisition card at a sampling rate of 12.8 kHz. The scatter plot of 2400 disturbance signals in the feature space of F2, F4 and F5 is shown in Fig. 4. It clearly indicates that the 11 PQ disturbances are separable and can be categorized into 7 clusters; first cluster denotes 3 disturbances of voltage interruption, voltage sag and swell. Second cluster
TABLE I RECOGNITION ACCURACY OF PQ DISTURBANCES Classes C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C C0 100 C1 100 C2 2 96 2 C3 95 3 2 C4 100 C5 100 C6 1 93 1 5 C7 3 89 8 C8 2 3 4 91 C9 3 2 95 C10 1 1 2 96 C11 4 2 94 Accuracy 100 100 96 95 100 100 93 89 91 95 96 94 (%)
TABLE II RECOGNITION ACCURACY AT DIFFERENT NOISE LEVELS classes Classification Accuracy (%) at Average different SNRs Accuracy 25 dB 30 dB 40 dB 55 dB 8 single disturbances 97 97 100 100 98. 8 single and 92 94 98 99 95. 3 combined disturbances
contains both notch and spike, and third one signifies the sag with harmonics and swell with harmonics. The first three clusters individually have a group of disturbances, whose characteristics are similar based on these three features. Now, the disturbances of these clusters can be easily distinguished among others of the same cluster with the help of other two features F1 and F3. The rest of the clusters represent a single power quality disturbance alone such as fourth - transient, fifth - flicker, sixth - flicker with harmonics and the last one harmonics. It can also be evident that the normal signals are at the origin as they have very slight deviation in amplitude (≈ 1 p.u.) and no harmonic distortion. The recognition accuracy for each class of disturbance is listed in Table I. It can be noticed that almost all the classes are recognized perfectly except the notch, spike and transient. The near similar characteristics of the signals are leading to misclassification among themselves like spike to transient and notch to spike. Further, the signals generated with parameters at boundary conditions and noise content is also a considerable reason for the misclassification. For instance, a few flicker with harmonic signals are partially misclassified as flicker or completely misclassified as swell with harmonics. Moreover, the proposed scheme has also been verified on signals having various noise levels as shown in Table II. It also presents the performance of the decision tree classifier with rules framed for classification of only single disturbances and other for classification of single and combined disturbances. In both the cases, the accuracy of the approach is reducing with an increase in the noise content, however the drop in accuracy is less. Also, it can be noticed that classification of 8 single disturbances alone is far better with an average accuracy of
TABLE III PERFORMANCE COMPARISON AT DIFFERENT NOISE LEVELS Classes Fast ST ADALINE and SSD and Proposed and DT [8] FFNN [10] DT [15] Method 50 dB 30 dB 50 dB 30 dB 50 dB 50 dB 30 dB C1 98.67 98.67 100 100 100 100 98 C2 96.67 96 100 98 100 98 97 C3 - - 100 99 100 97 96 C4 99.33 100 98 90 100 100 99 C5 - - 94 87 100 100 97 C6 100 99.33 98 86 100 97 91 C7 100 100 97 85 100 94 88 C8 100 100 97 90 100 97 89 C9 96 79.33 98 89 84.67 99 93 C10 - - 97 88 86 99 95 C11 100 100 94 85 91.33 98 92 Average 98.83 96.66 97.54 90.63 96.54 98.09 94.
around 98.5%, whereas it decreased to 95.75% with inclusion of three two-combination disturbances (C9, C10 and C11). Table III summarizes a comparison of results obtained with the proposed method and that reported in recent studies. The ANN based approach [10] proposed for classification of 96 exclusion combinations of PQ disturbances reports a minimum of 90 % accuracy for all combinations. However, the accuracy drops to 80 - 90 % under noisy conditions. Same is the case with the fast ST and DT approach [8] which utilizes a set of 20 features for classification of 13 PQ disturbances. The performance of sparse signal decomposition (SSD) with a hierarchical DT algorithm [15] is better in detection of single disturbances but the performance degrades for the combined disturbances of classes C9, C10 and C11. The comparative study reveals that the GEWT with the DT classifier is suitable enough to detect the most significant PQ disturbances both under noiseless and noisy conditions. The other feature which is also important for the PQ analysis is the computation time. The mean execution time for recognizing a PQ disturbance on a PC with 3.1 GHz processor and 2 GB RAM is found to be approximately 37.2 ms. Thus, it is feasible to implement the proposed method in real time for online detection of PQ disturbances. The advantages of the proposed approach can be summa- rized as
- Adaptive Filtering: The frequency estimation is according to the signal analyzed without requiring any prior infor- mation. The filter design is also adaptive with respect to the frequency components, making it suitable to analyze the PQ disturbances.
- Requires less number of features: Only five basic features, which significantly reflect the presence of disturbances have been selected and are able to enhance the perfor- mance of the classifier. The recognition accuracy can be further improved with inclusion of additional features but with an increased computations.
- Extendable for more classes: The proposed GEWT with the same features extracted can be extended to detect more combination of PQ disturbances by employing a non-linear classifier such as SVM, FL or ANN.
IV. CONCLUSIONS
This paper proposes a generalized EWT based feature ex- traction for classification of PQ disturbances. The classification of 11 PQ disturbances is performed with a simple rule based decision tree classifier. The GEWT with adaptive thresholds for frequency estimation and adaptive filter design is able to accurately decompose the signals. Moreover, the fundamental frequency component exactly reflects the change in ampli- tude, thereby the disturbances. The disturbances considered in the paper are eight single and three combined disturbances having fundamental frequency variation and noise. Finally, the approach has also been tested for three practical signals of harmonics with interharmonics and oscillatory transient. The GEWT with a simple DT classifier performs very well for recognition of most significant PQ disturbances at less computational cost.
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