Power Quality Monitoring of a Power System using Wavelet Transform

Transcription

1 International Journal of Electrical Engineering. ISSN Volume 3, Number 3 (2010), pp International Research Publication House Power Quality Monitoring of a Power System using Wavelet Transform Dr. A.K. Sinha #1, Meghna Barkakati #2, Dibakar Nath #3, Saurav Kumar Sarma #4, Uday Kumar Reddy #5 and Abhinav Verma #6 Department of Electrical Engineering, National Institute of Technology, Silchar, Assam , India 1 ashokesinha2001@yahoo.co.in, 2 meghnabarkakati@gmail.com 3 dibakar_datsme@yahoo.co.in, 4 skrs.elect123@gmail.com 5 urfrnuday@gmail.com, 6 abhinavrakeshverma@gmail.com Abstract In this paper, state space modeling is used to predict the exact nature of transient phenomena for transmission lines. An algorithm is developed to generate the fundamental wave during pre-transient, transient and posttransient phenomena for transmission lines. This paper also presents a software using MATLAB for the purpose of feature extraction in discrete wavelet transform (DWT) domain. The feature vector, thus obtained can be used as the input to the classifier for classifying the disturbance type and monitoring of power system. Index Terms: Power quality, wavelet transform, state space modeling, feature extraction. Introduction Utilities all over the world have for decades worked on the improvement of what is now known as power quality. The recent interest in power quality can be explained in a number of ways [1]. Electronic and power electronic equipment has become much more sensitive than its counter parts 10 to 20 years ago. Disturbances like impulse and sags pose as a great danger to electronic equipment. They can make the voltage or current waveform abnormal, which could interrupt sensitive users and result in very expensive consequences thus degrade their performance and efficiency [2]. Conscious customers now turn to the local utility to identify the problem. Presently, many utilities maintain dedicated engineers to address customers power quality concerns and to provide appropriate mitigation procedures. In order to improve the quality of

2 190 A.K. Sinha et al power, electric utilities continuously monitor power delivered at customer sites. The detection and classification are therefore essential to identify the cause and source of the disturbances so that their effect can be neutralized using suitable corrective and preventive measures. During a fault on a multiconductor transmission line, the fundamental waveform gets contaminated with significant number of travelling and electromagnetic waves [3]. The fault transient waveform depends on frequency variable parameters such as line length, conductor configuration and earth return path. A d.c. component predominates for faults occurring at the instant of voltage zero-crossing. Because of the complexity of the power system and type of faults, it is extremely difficult to model such non linear waveforms. The present work deals with a method of simulation of a single phase transmission line with lumped parameters by using state space modelling. Wavelet Transformation Technique Many investigations in the field of Wavelet Transform (WT) as a tool for detection of Power Quality Disturbances have been reported in the past [4,5,6,7,8,9]. This method is developed using the Discrete Wavelet Transformation (DWT) analysis. The given transient signal is decomposed through wavelet transform and any change in the smoothness of the signal is detected at the finer wavelet transform resolution level. Later the energy distribution pattern of the given signal is evaluated and a relationship between this evaluated energy distribution pattern and that of the corresponding pretransient fundamental component is established. This study shows that each power quality disturbance has unique deviation from the fundamental waveform and this is adopted to provide a reliable classification of the type of disturbance. The discrete wavelet transform (DWT) is one of the three forms of wavelet transform. It moves a time domain discritized signal into its corresponding wavelet domain. This is done through a process called sub-band codification, which is done through digital filter techniques[8]. In the signal processing theory, to filter a given signal f(n) means to make a convolution of this signal. This is illustrated in Fig. 1. The f(n) signal is passed through a low-pass digital filter (h d (n)) and a high-pass digital filter (g d (n)). After that, half of the signal samples are eliminated. This is indicated by the symbol 2 in Fig. 1. Figure 1: Sub Band Codification Scheme of a Signal.

3 Power Quality Monitoring of a Power System using Wavelet Transform 191 Basically, the DWT evaluation has two stages. The first consists on the wavelet coefficients determination. These coefficients represent the given signal in the wavelet domain. From these coefficients, the second stage is achieved with the calculation of both the approximated and the detailed version of the original signal, in different levels of resolutions, in the time domain [8]. At the end of the first level signal decomposition, the resultant vectors y h (k) and y g (k) will be the level 1 wavelet coefficients of approximation and of detail. In fact, for the first level, these wavelet coefficients are called c 1 (n) and d 1 (n) as stated below. (1) Next, in the same way, the calculation of the approximated (c 2 (n)) and the detailed (d 2 (n)) version associated to the level 2 is based on the level 1 wavelet coefficient of approximation (c 1 (n)). The process goes on, always adopting the n-1 wavelet coefficient of approximation to calculate the n approximated and detailed wavelet coefficients. Once all the wavelet coefficients are known, the discrete wavelet transform in the time domain can be determined. This is achieved by rebuilding the corresponding wavelet coefficients along the different Resolution levels. By using the DWT and observing the particular features of the several decomposition levels of a signal, some important conclusions of it can be drawn. This information can be used to detect, to locate and to classify the disturbance. A digital program was developed and implemented in the wavelet toolbox of the MATLAB platform. (2) Choice of Mother Wavelet The choice of mother wavelet plays a significant role in detecting and localizing various types of disturbances. Daubechies wavelets with 4, 6, 8,10 and 12 filter coefficients work well in most disturbance detection cases. However for some disturbances, such as sag or overvoltage disturbances (within 5%), Daubechies wavelet with different filter coefficients can detect or localize different kinds of disturbances. Therefore, the choice of the mother wavelet is important. In power quality disturbance detection, generally, one can classify disturbances into two categories, fast and slow transients. In the fast transient case, the waveforms are marked with sharp edges, abrupt and rapid changes, and a fairly short duration in time. In this case, Daub4 and Daub6, due to their compactness, are particularly good in detecting and localizing such disturbances. In the slow transient case, the waveforms are marked with a slow change or smooth amplitude change. Daub4 and Daub6 may not be able to catch such disturbances, since the time-interval in integral evaluated at point n is very short. However, if Daub8, Daub10 and Daub12 are used, the time interval integral is long enough and, thus, such wavelets can sense the slow changes.

4 192 A.K. Sinha et al Digital simulation A simulation method of a single phase transmission line is carried out with lumped parameters by using state-space modeling. State space modeling A single phase equivalent pi section transmission line having source inductance L 1,series resistance R 1, series inductance L 2, shunt capacitance C 1 and C 2 at both ends and load R 2 is shown in Fig. 2. Figure 2: Pre-fault circuit diagram of a single phase line. Let the state variables be : x 1 = i 1 = current in L 1 x 2 = i 2 = current in L 2 x 3 = v c1 = voltage across C 1 x 4 = v c2 = voltage across C 2 Taking mesh current or node voltage equations of the pre-fault circuit, it is possible to write: Consider a fault at a point with a fault resistance R f. the pre-fault network is converted into post fault network as shown in Fig 3. The fault resistance R f is small and value of C 2 is almost negligible. (3) Figure 3: Post fault circuit diagram.

5 Power Quality Monitoring of a Power System using Wavelet Transform 193 Taking mesh current or node voltage equation of the post fault circuit, it is possible to write again: ( ) 1 x L 1 1 x1 L1 R1+ R3 1 x2 = 0 ( ) x2 + 0 [ Vs ] L1 L 2 x 3 0 x3 1 1 ( ) 0 C1 C1 (4) RR f 2 R3 = ( ) R f + R2 Where Equations (3) and (4) are in the form of continuous time state equation as follows: x() t = Ax() t + Bu() t (5) Equation (5) is converted into a discrete time state equation as x( m+ 1) = φ( T ) x( m) +Δ( T ) x( m) s s (6) Where, T s is sampling time. The sampling frequency is taken as 1200 Hz. Algorithm The waveforms under normal condition are directly obtained by representing the single phase system in the state space model. On the other hand, the transient waveforms of voltage and current are obtained by superimposing fundamental and harmonic components proportioned by experience. An algorithm has been developed for computing pre-fault and post-fault waveforms (presuming various harmonics). The single phase power system described earlier is represented in the form of continuous state model equation as in equation (5). The discretization of the state space model is carried out to make the digital simulation easier [3]. To achieve this vector-matrix differential equation of the continuous time system is converted into a discrete time system as given by equation (6).The whole simulation process is shown in the fig.4. Figure 4: Diagrammatical representation of digital simulation process.

6 194 A.K. Sinha et al Figure 5: Flowchart for algorithm. The digital simulation flowchart as shown in fig.5 is carried out extensively with various effects to cover the actual situations of power system. Pre-fault simulation The simulated pre-fault line voltage and current waveforms are shown in Fig. 6 Figure 6: Fundamental voltage and current waveforms. Post-fault simulation In the post-fault condition, the effect of fault-resistance, fault-instance and load are studied and related waveforms are generated. The simulated post-fault line voltage and current waveforms are shown in Fig. 7(a) and Fig. 7(b).

7 Power Quality Monitoring of a Power System using Wavelet Transform 195 Figure 7(a): Post fault voltage waveform. Figure 7(b): Post fault current waveform. Low pass filters A very contemporary method of filtering noisy or distorted signal waveforms has been taken up for a comparative analysis with the filtering technique which is dealt with in this paper. A 3 rd order Butterworth low-pass filter has been used to filter out the harmonics. The filter used is a recursive type, i.e. its output depends on both present and past inputs as well as past outputs. In this study digital low pass filter have been designed by using bilinear transformation method and then implemented. The transfer function of recursive low pass filter is given by : 1 H() s = 3 2 s + 2s + 2s+ 1 (7) Where z + 1 s = z 1 Figure 8: Low-pass filtered voltage waveforms. Figure 9: Low-pass filtered current waveforms. From the above fig.8 and fig.9 it can be concluded that the current and voltage waveforms both show a phase shift as the low pass filter is a frequency domain representation. As a result of which there a phase shift in the time domain. The low pass filtered waveform is further seen to have reduced the amplitude compared to the fundamental waveform. Now in order to do away with these problems, wavelet transform is used to filter out the higher order harmonics in the fundamental voltage

8 196 A.K. Sinha et al and current waveform. As wavelet transform is a time as well as frequency representation of a signal, the problem of phase shift is expected to be absent. The following section deals with wavelet transform. Wavelet transform The choice of mother wavelet affects the detection and localization of various types of power quality disturbances. For the purpose of detecting harmonics and reconstructing the waveform after denoising it Daub 12 is found to be the most appropriate mother wavelet for this work. Figure 10: Comparison of fundamental and wavelet filtered voltage waveform. Figure 11: Comparison of fundamental and wavelet filtered current waveform. It is seen from the above fig.10 and fig.11 that the wavelet transform is successful in eliminating the transients in the voltage and current waveforms without any phase shift. However there is a slight change in the amplitude of the waveforms which is caused due to the occurrence of the fault. There is a dip in voltage due to the fault whereas there is a swell in the current due to decrease in effective resistance of the circuit. Feature Extraction The wavelet transform is an effective tool for the analysis of power quality disturbances [11]. In the following section, the procedure of feature extraction, for detection, localization and classification of various power quality disturbances is described. We first use (Discrete Wavelet Transform) DWT and (Multi Resolution Analysis) MRA technique the pre fault and post fault signal to decompose them up to a fixed resolution level J. The DWT of discrete time sequence f(k) results in a multiresolution characterization of f(k). The resulting signal decomposition generates detail and approximate coefficients [d 1, d 2,.,d J, c J ] which are the DWT representation of signal f (k ). Here d m and c m are the vectors representing detail and approximation coefficients at any resolution level m and m belongs to (1, J). The discontinuities in the signal due to disturbances in the form of any irregularity will be reflected in the detail coefficients at the finer levels. This provides an easy means to detect the disturbance. The squared wavelet coefficients at different resolution levels,

9 Power Quality Monitoring of a Power System using Wavelet Transform 197 the standard deviation and/or mean value and maximum modulus of wavelet coefficients at different resolution levels, are the some of the used features derived from wavelet coefficients. Recently, energy distribution of the distorted signal at different resolutions has emerged as very efficient discriminatory features. The energy of distorted signal at some resolution level m can obtained as = (8) where, N m is the number of available wavelet coefficient at resolution level m [11]. To test the effectiveness of the proposed scheme of the wavelet based PQ monitoring system under practical pre-fault waveform and post-fault waveform, the energy distribution patterns for fundamental pre-fault current waveform and post-fault waveform are studied. All the simulated waveforms were obtained for a power frequency of 50Hz, and for a sampling frequency of 1200Hz. Figure 12: Energy distribution pattern in DWT up to 10 th levels. Fig.12 shows the detail energy distribution of a pure sine current wave up to 10 th scale in wavelet domain. Here 5 th resolution represents the fundamental frequency. To display clearly the energy patterns, the energy distribution of the first three frequency bands and the rest of the seven lower frequency bands are re-plot in Fig. 13 and Fig. 14 respectively. Figure 13: First three energy distribution pattern in DWT pattern. Figure 14: The energy distribution pattern in DWT domain for last 7 levels for the fundamental waveform.

10 198 A.K. Sinha et al Figure 15: First three energy distribution pattern in DWT pattern for transient current waveform. Figure 16: The energy distribution pattern in DWT domain for last 7 levels. Fig 15 and Fig.16 show the energy distribution pattern for current waveform after the fault. It is seen from these figures that the presence of transients change the energy distribution pattern at higher frequency bands and its effect on energy distribution decreases as one moves from higher to lower frequency bands. It is thus seen, in case of any disturbance such as transients or any other deviation from rated values, the energy distribution pattern changes. The type of the disturbance can be assessed by observing the energy patterns at different frequency bands. Conclusion The state space simulation of the transmission line has been successfully carried out with the help of real time algorithm. This algorithm can be used to predict the exact nature of transient phenomenon for transmission lines. This method generates a continuous fundamental waveform before transient, during transient and after transient conditions. Using wavelet transform, fundamental voltage and current of the power system for above three dynamic conditions are extracted. It thus enables continuous monitoring of the quality of power system. This can be further utilized for high voltage three-phase power system. This paper has also addressed the effect of harmonics on the energy features in wavelet domain extracted for detection and classification power quality disturbances. This technique can be applied to a wide variety of power quality signals by analyzing the change in energy distribution pattern in wavelet domain. The energy feature vector obtained in the paper can be used as an input to the classifier for classifying the disturbance type. AI based methods like neural networks, fuzzy and neuro-fuzzy networks can be used for this purpose. Acknowledgement We would like to acknowledge the Electrical Engineering Department, N.I.T Silchar for allowing us to do the research work.

11 Power Quality Monitoring of a Power System using Wavelet Transform 199 References [1] Math H. J. Bollen and P. M. Anderson, Understanding Power Quality problems, IEEE Press, New York, pp.1-22 [2] Roger C. Dugan, Mark F. McGranaghan, Surya Santoso, H.Wayne Beaty, Electrical Power Systems Quality, Mc Graw- Hill, pp [3] Dr.A.K.Sinha, S.Sinha and P.B.Dutta Gupta, Digital Simulation Of Faulted EHV Transmission Lines for Multiprocessor based Distance Relaying Applications,Electrical Power Systems modeling and simulation, J.Robert, W. Midvidy(editors), J.C. Baltzer AG, Scientific Publishing Co., IMACS 1989, pp [4] Surya Santoso, Edward J. Powers, and W. Mack Grady, Electric Power Quality Disturbance Detection Using Wavelet Transform Analysis. [5] Roger C.Dugan,Mark F. McGranaghan,Surya Santoso,H.Wayne Betay, Electrical Power Systems Quality,Mc Graw-Hill,2002,p [6] J. S. Huang, M. Negnevitsky and D. T. Nguyen, Wavelet Transform Based Harmonic Analysis. [7] Surya Santoso, Edward J. Powers, and W. Mack Grady and Antony C. Parsons, Power Quality Disturbance Waveform Recognition Using Wavelet- Based Neural Classifier Part 1: Theoretical Foundation, in IEEE transactions on power delivery, vol. 15, no. 1, January [8] Resende, J.W., Chaves, M.L.R. and Penna, C., Identification of power quality disturbances using the MATLAB wavelet transforms toolbox. [9] Ricardo A. Lima, Claudio A. Reineri and Fernando H. Magnago Hybrid Power Quality Harmonic Analysis. [10] Thomas Croes, Cristina Gherasim, Jeroen Van den Keybus and Jozef Ghijselen, Power Measurement Using Wavelet Transform of Analytic Signals, in th International Conference on Harmonics and Quality of Power. [11] U. D. Dwivedi, and S. N. Singh,, A Robust Energy Features Estimation for Detection and Classification of Power Quality Disturbances, 2006 Matlab Help.

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