Selection of Mother Wavelet for Processing of Power Quality Disturbance Signals using Energy for Wavelet Packet Decomposition

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1 Volume 114 No , ISSN: (printed version); ISSN: (on-line version) url: ijpam.eu Selection of Mother Wavelet for Processing of Power Quality Disturbance Signals using Energy for Wavelet Packet Decomposition M.S.Priyadarshini 1 and M. Sushama 1 J.N.T.U Anantapur, Ananthapuramu 5152, India mspriyadarshini.raj@gmail.com 2 J.N.T.U.H College of Engineering, Hyderabad 585, India m73sushama@jntuh.ac.in Abstract Electric power that is transmitted and distributed must be free of disturbances. The disturbances that affect the quality of electric power supplied are termed as power quality disturbances. For information extraction, it is necessary to employ signal processing methods for these signals. The signals considered for analysis are voltage sag, swell, interruption, harmonics, transient, fluctuations and flicker. In this paper, an attempt is made to process the disturbance signals by using wavelet packet transform. Wavelet packet decomposition is used for decomposing each power quality disturbance signal to five levels and energy for wavelet packet decomposition values using all types of entropy are obtained for each signal. The obtained energy values are compared with energy for wavelet packet decomposition of sinusoidal voltage signal, which is used as a reference. Error in the energy values are obtained in MATLAB environment for each level and mother wavelet is identified for large 313 error values.

2 AMS Subject Classification: 42C4, 65T6, 94A12, 94A17. Key Words and Phrases: Energy; Entropy; Mother wavelet; Power quality disturbances; Wavelet Packet Decomposition. 1 Introduction IEEE standard , IEEE Recommended practice for monitoring electric power quality defined different power quality disturbances for efficient power quality monitoring of a power system network. The disturbances result in deviation of voltage or current from an ideal sinusoidal waveform. Any deviation of voltage or current from the ideal is a power quality disturbance [1]. The signal processing method of wavelet packet analysis is used. In wavelet packet analysis, the approximations as well as the details can be split into next level approximation and detail [2]. Approximations are low frequency and details are high frequency representation of the original signal. By using a suitable function in MATLAB, the energy values of approximations and details are obtained for each node of wavelet packet tree. The paper is organized as section 2 with an explanation about the considered power quality disturbances, and section 3 dealing with wavelet packet decomposition based analysis of the signals using suitable function for energy in MATLAB command line interface. Section 4 explains about selection of mother wavelet from the obtained error in energy values and section 5 ends with conclusion. 2 Power Quality Disturbance Signals The power quality disturbances considered are sag, swell, interruption, harmonics, transient, fluctuations and flicker. All these disturbances can cause adverse effects on the quality of electric power supplied by the utilities. The applied voltage across the loads must be constant in magnitude and frequency representing a pure sinusoidal signal shown in fig.1. Due to any of the power quality disturbances, this condition cannot hold good. A sag is a decrease in root mean square voltage to between.1 per unit and.9 per unit for durations from.5 cycles to 1 minute [3]. Per unit value is defined as ratio of actual value to base value of voltage is denoted as per unit. The possible causes of sags are startup loads and faults, swells are load changes and utility faults and interruption are switching, utility faults, circuit breaker tripping, and component failures [4]. A swell is an increase in root mean square voltage above 1.1 per unit for durations from.5 cycle to 1 minute. Typical magnitudes are between per unit to 1.8 per unit [3]. An interruption occurs when

3 the supply voltage or load current decreases to less than.1 per unit for a period of time not exceeding 1 minute [3]. Sag, swell and interruption respectively indicate decrease, increase and loss of voltage for a certain period as shown in fig.1. Harmonics are sinusoidal voltages or currents having frequencies that are integer multiples of the frequency at which the supply system is designed to operate (termed as fundamental frequency) [3]. Waveform generated for harmonics has fundamental frequency (5 Hz) in addition with frequencies of third (15 Hz), fifth (25 Hz), and seventh order (35 Hz). Sine voltage Voltage swell Harmonics Fluctuations Voltage sag Voltage interruption Transient Voltage flicker Fig. 1. Sinusoidal voltage signal and different types of power quality disturbances with time in milliseconds on x-axis and magnitude of voltage in per unit on y-axis. This shows a figure consisting of voltage sag, swell, interruption, harmonics, transient, fluctuations and flicker signals which are termed as power quality disturbance signals. A transient can be a unidirectional impulse of either polarity or a damped oscillatory wave with the first peak occurring in either polarity [3]. The possible causes of transients, shown in fig.1, are lightning, electrostatic discharge, utility fault clearing, and switching of inductive or capacitive loads [4]. Transient signal will be a function magnitude, settling time and frequency of transient and angular transient frequency. Fluctuations are systematic variations of the voltage envelope or a series of random voltage changes, the magnitude of which does not normally exceed the voltage ranges of.95 per unit to 1.5 per unit [3]. The possible causes of voltage fluctuations are radio transmitters, faulty equipment, ineffective grounding, and proximity to electromagnetic interference and radio frequency interference [4]. The waveform for fluctuations is shown in fig.1. Loads that exhibit continuous, rapid variations in load 315 current magnitude can cause voltage variations erroneously

4 referred to as flicker and the term flicker is derived from the impact of the voltage fluctuation on lighting intensity [3]. Flicker is depicted in fig. 1. For analysis of all these disturbances, signal processing method of wavelet packet analysis is employed. 3 Wavelet Packet Decomposition Wavelets have been realized as a very powerful auxiliary tool in the storage and analysis of problematic power quality waveforms and signals [5]. Wavelet transform analyses a stationary signal that decomposes a signal into different scales with different levels of resolution by dilating a single prototype function termed as mother wavelet [6]. In [6], multiresolution signal decomposition technique is used for decomposing a signal into its details and approximations. Daubechies wavelet of order 4 (db4), Daubechies wavelet of order 1 (db1), Symlet wavelet of order 5 (sym5), Discrete Meyer wavelet (DMeyer i.e., dmey), Coiflet wavelet of order 5 (coif5), and Daubechies wavelet of order 1 (db1) are the wavelets used respectively. In [7], energy and entropy parameters associated with wavelet packet transform are used for automatic classification of signals and also for detection of voltage disturbances in electric signals. In [8], the percentage ratio of the energy of the distorted signal to the energy of the reference signal is calculated using db4, db6, db4, coif1, coif5, sym2 and sym8 mother wavelets at each frequency band. (, ) original signal (1, ) (1, 1) Level 1 (2, ) (2, 1) (2, 2) (2, 3) Level 2 Fig. 2. Wavelet packet tree for two level decomposition. The first terms in node labels 1 and 2 indicate first and second levels of decomposition. In node labels, the second terms in node labels and 2 indicate approximations and 1 and 3 indicate details. The discrete wavelet transform is defined as [6], ( ) ( ) ( ) (1) In (1), the discretized mother wavelet is given as, ( ) ( ( ) ) (2) 316 The scaling and translation parameters with positive

5 integers m and n are discretized respectively as and, where, [6]. Information about the signal can be obtained from approximations and details shown in fig.2. Energy values are obtained for all the first, second, third, fourth and fifth levels of decomposition using db4, db1, sym5, dmey, coif5 and db1 wavelets. Energy values for wavelet packet decomposition using six wavelets are obtained for each decomposition level of one to five. Difference in energy for wavelet decomposition values are calculated for each level using different wavelets. The differences are termed as error values calculated by the difference of actual values and measured values. Actual values refer to energy values of sine signal considered as reference. Measured values refer to energy values of power quality disturbance signals sag, swell, interruption, harmonics, transient, fluctuations and flicker. For each disturbance and each wavelet used, maximum error values are obtained for fifth level and are shown in table 1. From the obtained energy error values using six mother wavelets only the maximum values are chosen. 4 Energy for Wavelet Packet Decomposition The function wenergy is described as energy for wavelet packet decomposition under wavelet packet algorithms. For a wavelet packet tree, the function wenergy returns a vector which contains the percentage of energy corresponding to the terminal nodes of the tree [2]. The maximum allowed decomposition level for the power quality disturbance signals is 1 and is obtained by using the function wmaxlev, taking into consideration the size of the signal. In general, a smaller value of 5 is taken for one-dimensional case. So wavelet packet tree is decomposed into 5 levels. The length of all the signals is 41. The analysis decomposition function wpdec is used for full decomposition purpose in wavelet packet analysis [2]. The function takes into consideration the signal, level of decomposition, mother wavelet and entropy. If entropy is not mentioned, Shannon entropy is considered. Entropy is used for feature extraction. Entropy refers to Shannon, log energy, norm, threshold and SURE entropy. For norm, threshold and SURE entropy, an additional value of parameter is to be specified. The number of nodes in first, second, third, fourth and fifth level decompositions are 2, 4, 8, 16 and 32 respectively. If wavelet decomposition is used for processing of the signals, percentage of energy corresponding to the approximation and details will be returned.the term signal represents each of sinusoidal voltage, sag, swell, interruption, harmonics, transient, fluctuations and flicker signals generated for time 317

6 of length 41 elements. The signals are generated using mathematical equations governing each disturbance. Table 1. Maximum error values for fifth level decomposition. Signal db4 db1 sym5 dmey coif5 db1 Sag Swell Interruption Harmonics Transient Fluctuations Flicker As one dimensional five level wavelet packet decomposition is used for the processing of power quality disturbance signals, 32 values are returned pertaining to the 32 terminal nodes of both the signals. For 5 level decomposition of wavelet packet tree, there will be 32 terminal nodes labeled as (5, ) up to (5, 31). The energy for each node is obtained by using the function wenergy in command line analysis of MATLAB. For example, an interruption signal is representing a loss of voltage for a very short duration where as a sine signal is a smooth continuous signal. The energy values for all the signals are determined and the error in energy values obtained as a difference of energy values of sine and energy values of disturbance signal are calculated. Mother wavelets used for analysis are from Daubechies, Symlet and Coiflet families i.e., db1, db4, db1, dmey, sym5, and coif5 wavelets. For fifth level of wavelet packet decomposition, the energy values for nodes, 2, 4, 6, 8, 1, 12, 14, 16, 18, 2, 22, 24, 26, 28, 3 and 32 correspond to approximations and the energy values for nodes 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 and 31 correspond to details. The available entropy criteria are Shannon entropy, log energy entropy, norm entropy, threshold entropy and SURE entropy [2]. The entropy values can also be calculated using command line function wentropy. Shannon entropy is nonnormalized entropy involving the logarithm of the squared value of each signal sample given as, ( ) [2]. Log energy entropy is the logarithm of energy entropy, defined as the sum over all samples given as, ( ) [2]. The concentration in norm with [2]. The norm entropy vales are always positive. The parameter for calculating norm entropy values is taken as 1.5. Threshold entropy is described as the number of samples for which the absolute value of the signal exceeds a threshold ε [2]. Threshold value is chosen as.5 as the parameter representing threshold value is. SURE (Stein s Unbiased Risk Estimate) is a threshold-based entropy in which the threshold equals ( ( )), where is the number of samples in the signal [2]. The entropy used can be 318

7 any one of the above types defined. The command function for energy is in terms of entropy. In [9], by using different entropy types, a classification is obtained between sag, swell and interruption signals with respect to a pure sine signal. 5 Selection of Mother Wavelet The selection of the best wavelet wavelets is a function of the characteristics of the signal to be processed [1]. In order to select suitable mother wavelet, from the obtained error values a comparison is done for all the 264 error values. In (3), 2, 4, 8, 16 and 32 stand for the number of terminal nodes for first, second, third, fourth and fifth levels of decomposition respectively. The number of power quality disturbances considered are 7 and the number of different wavelets chosen are 6. ( ) multiplied by product of 7 and 6 gives 264. From all 264 values it is observed that out of all the maximum values corresponding to each level, the highest error in energy values are obtained for fifth level values shown in table 2. Table 2. Highest values in maximum error values corresponding to fifth level out of all levels of decomposition. power quality disturbance signals Values using Shannon and Threshold entropymother wavelet used Values using Log energy, Norm and SURE entropy - mother wavelet used Sag coif coif5 Swell.11 - coif coif5 Interruption coif coif5 Harmonics coif coif5 Transient sym sym5 Fluctuations db coif5 Flicker db db1 The difference in energy value is high using coif5 wavelet and all the five types of entropy for sag, swell, interruption and harmonics. The difference in energy value is high using sym5 wavelet and all the five types of entropy for transient signal. The difference in energy value is high using db1 wavelet and Shannon, threshold entropy for fluctuations signal. The difference in energy value is high using db1 wavelet and all the five types of entropy for flicker signal. 6 Conclusion The power quality disturbance signals considered for analysis are voltage sag, swell, interruption, harmonics, transient, fluctuations and flicker. In order to analyze the power quality disturbance signals wavelet packet decomposition for five levels is used with db4, db1, sym5, dmey, coif5 and db1 wavelets as mother wavelets, for signal processing to obtain information 319 about the type of wavelet

8 suitable for each of the signals. The voltage signals are generated in MATLAB and wavelet packet analysis is carried out to obtain energy values using the MATLAB function wenergy. Error between the energy values of sine signal, used as reference, and each power quality disturbance are calculated. The maximum values are identified and suitable mother wavelet is selected for each disturbance. When the error value is large compared to a smaller value, it indicates that the mother wavelet used is effective in identifying the disturbances present in the signal. References 1. Math H.J. Bollen and Irene Y.H. Gu.: Signal Processing of Power Quality Disturbances. Wiley-IEEE Press, New York, U.S.A (26) 2. M. Misiti, Y. Misiti, G. Oppenheim, J-M. Poggi: Wavelet Toolbox for use with MATLAB- User s guide. Version 3, Math works Inc. (26) 3. IEEE Standard : IEEE Recommended Practice for Monitoring Electric Power Quality, IEEE Power and Energy Society (1995) 4. Seymour Joseph: The seven types of power quality problems. White paper 18, Revision 1, pp. 1-21, Schneider Electric White Paper Library (211) 5. Wael R. Anis Ibrahim and Medhat M. Morcos: Artificial Intelligence and Advanced Mathematical Tools for Power Quality Applications: A Survey. IEEE Transactions on Power Delivery Vol. 17, No. 2, pp (22) 6. Santoso S, Powers E.J, Grady W.M, and Hofmann P: Power quality assessment via wavelet transform analysis. IEEE Transactions on. Power Delivery, vol. 11, no. 2, pp (1996) 7. Varnis M and Pederiva R: Wavelet Packet Energy-Entropy Feature Extraction and Principal Component Analysis for Signal Classification. Proceeding Services of the Brazilian Society of Applied and Computational Mathematics, Vol.3, N.1, pp. 1-7 (215) 8. Gargoom A.M, Ertugrul N, and Soong W.L: Comparative Study of using Different Mother Wavelets on Power Quality Monitoring. In: Australasian Universities Power Engineering Conference (AUPEC 24), Paper ID 96, Australia (24) 9. Priyadarshini M.S and Sushama M: Classification of Short- Duration Voltage Variations using Wavelet Decomposition based Entropy Criteria. In: IEEE Conference on Wireless Communications, Signal processing and networking, pp , India (216) 32

9 1. Galli A.W, Heydt G.T and Ribeiro P.F: Exploring the Power of Wavelet Analysis. IEEE Computer Applications in Power, Vol. 9, Issue: 4, pp (1996) 321

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