CHARACTERIZATION OF TRANSMISSION LINE FAULTS USING ALGORITHM BASED WAVELET TRANSFORMS
P. RAM KISHORE KUMAR REDDY
Associate Professor, Department of EEE, MGIT, Hyderabad, Andhra Pradesh, India
ABSTRACT
Detection of the disturbances by protective devices is very much required l for improving the performance of the power systems. The disturbances in power systems reduce the quality of power and in turn the life time of the equipment.
Thus it requires detection and classification of the faults by using refined methods. In this paper signal processing tool such as algorithm based Wavelet Transforms have been used to obtain the detailed and approximate coefficients of the fault signal. These coefficients are used to characterize the different types of the disturbances. Algorithm based wavelet transform provides better in-depth analysis as compared to Fourier Transforms. The magnitudes of the detailed and approximate coefficients are very much useful to realize the different types of the disturbances.
KEYWORDS: Multi, Resolution Analysis, Wavelet Transforms Detailed and Approximate Coefficients, Fault Classification
INTRODUCTION
Transmission lines protection is vital to achieve reliable transmission electrical power system. Faults on transmission lines should be identified for proper operation of the power system. Analysis of fault event enable design of protective equipment and even gives the measure of insulation level. Identification of faults must happen in quick time so that quick and appropriate restoration steps can be taken immediately to restore reliable operation of the power system.
Existing deterministic methods do not have the ability to adapt to the system operating conditions and thus causes delay in identification of the faults and in turn their characterization.
The conventional method such as Fourier Transform cannot extract the exact features of the Fault signal because of the lack of time localization property of the Transform. More over FT will not provide the information regarding what frequency components exist in the signal along with the information about time instant. Therefore refined method needs to be proposed to identify and characterize the fault signal
The proposed method to overcome the difficulty Wavelet transforms which implements multi resolution analysis.
In this paper an algorithm is developed based on mathematical expression of the transform which provides information regarding the detailed and approximate coefficients of the faulted signal. This is the process of obtaining the features of the faulted signal such as L-L, L-L-LG, L-L-L-, L-L-L-G faults which have been simulated in MATLAB/ SIMULINK environment.
WAVELET TRANSFORMS
The basic idea of using wavelet transform is to analyze the fault signal at dissimilar scales or resolution called multi resolution analysis. Wavelets are a class of functions used to localize a given signal in both space and scaling ISSN(P): 2250-155X; ISSN(E): 2278-943X
Vol. 4, Issue 2, Apr 2014, 153-158
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domains. Compared to windowed Fourier analysis, the basis wavelet is stretched or compressed to synchronize the size of the window. Therefore, wavelets automatically adapt to both the high frequency and the low-frequency components of a signal by different sizes of windows. Any small change in the wavelet representation produces a correspondingly small change in the original signal, which means local disturbances do not influence the entire transform [3]. The wavelet transform is suitable for analyzing non-stationary signals such as voltage sag, swell, transients, flicker etc. Wavelets are functions generated by dilations and translations of a single function ψ called a mother wavelet,
The fundamental idea of wavelet transform is to represent any arbitrary function ‘f’ as a decomposition of the wavelet basis or write ‘f’ as an integral over a and b of ψa,b. Wavelet Transform (WT) is applied to analyze non-stationary signals, i.e., whose frequency response varies in time . Although the time and frequency resolution problems are results of a physical phenomenon and exist regardless of the transform used, it is possible to analyze any signal by using an alternative approach called the multi resolution analysis (MRA). MRA analyzes the signal at different frequencies with different resolutions. MRA are basically designed to give good time resolution and poor frequency resolution at high frequencies and good frequency resolution and poor time resolution at low frequencies[6] . Thus the approach is useful especially when the signal considered has high frequency components for short durations and low frequency components for long durations such as voltage sag.
One way to built sub-band codification is to split the spectrum into frequency bands which consumes more processing time. Therefore it is convenient to split the given signal into two bands of spectral components such as low pass filtered and high pass filtered components. The high pass filtered components gives the smallest information where as low pass filtered components gives information regarding further minutely varying details until desired number of bands.
Figure 1: Implementation of One Stage Iterated Filter Bank
The process of splitting the spectrum is represented in figure 1. The advantage of this scheme is that it is necessary to design only two filters and the disadvantage is that the signal spectrum coverage is fixed. For a sample current signal with a noise parameter the decomposition is shown in figure 2. The detail coefficients cD are consisting high-frequency content and the approximation coefficients cA contain the low frequency content of the signal. The actual lengths of the detail and approximation coefficient vectors are slightly more than half the length of the original signal.
This has to do with the filtering process, which is implemented by convolving the signal with a filter.
Figure 2: Decomposition of Signal with Noise Showing cD and cA
By observing the features obtained by Discrete Wavelet Transform (DWT) it is easy to detect, locate and classify the power quality disturbances. This MRA can be performed by Discrete Wavelet Transform (DWT).
CHARACTRIZATION OF FAULTS BY WAVELET TRANSFORMS
Different voltage faults have been simulated in MATLAB environment with the following simulink model.
Figure 3: Simulink Model for Simulating Faults
The healthy signal (without fault in the system) with 50Hz is simulated for the purpose of the analysis
Figure 4: The Healthy Signal (without Fault in the System) with 50Hz
In order to extract the features of the signal WT is used and consequently detailed and approximate coefficients are obtained. The magnitude of the WT coefficients signifies the degree of intensity of the disturbance of the signal [4]. In applying WT, the mother wavelet will be shifted with respect to the signal to be analyzed at every instant and while doing so the scaling function of the mother wavelet is synchronized according to the fault signal. For every shift in the mother wavelet and change in the scaling of the mother wavelet, detail coefficients and approximate coefficients are obtained [1].
To realize this procedure algorithm is developed to obtain the WT coefficient.
The healthy signal is decomposed at different stages by using WT algorithm and it can be observed that the decomposed signal is not having spikes and thus it can be concluded that the signal is not having the disturbance [2].
Figure 5: Decomposition of the Healthy Signal
By using the MATLAB simulink model, L-G fault is simulated as shown in the figure 6
Figure 6: L G Fault
Whenever a sudden short circuit occurs between the line and ground, the voltage profile[5] will be changed in the nearest adjacent feeder is illustrated. To identify the location at the instant at which the fault is occurring WT is applied as shown in the figure 7.
Figure 7: Detailed Coefficients of L-G Fault
Similarly WT algorithm is applied to various faults of the power system to obtain the Detailed and approximate coefficients as shown in figure 8 as an illustration for one fault
Figure 8: Stem Representations of Detailed Coefficients of Signal
The developed algorithm to realize WT is given below as an illustration to get filter coefficients. Observing carefully ,with the help of high pass and low pass filters it is possible to realize the algorithm for the WT.This is because due to MRA, up sampling and down sampling of the signal is adopted to analyze the signal
%Time domain plots of signal and filters figure;
subplot(311);
plot(x,'r');axis([0 lnx min(x) max(x)]);xlabel('time');,ylabel('Amplitude');
Title('Original signal');
subplot(312);
stem(lp);axis([0 length(lp) (min(lp)+0.1) (max(lp)+0.1)]);
ylabel('lp');
Title('Low-pass filter coefficients');
subplot(313);
stem(hp);axis([0 length(hp) min(hp)+0.1 max(hp)+0.1]);
ylabel('hp');
Title ('High-pass filter coefficients');%pause CONCLUSIONS
The algorithm is fast since wavelet can represent characteristic of a signal by reducing the redundancy of coefficients because of the localization property of the wavelet transform. Voltage disturbance detection and its characterization is very vital in determining the severity of the disturbance especially in deciding the power quality of the system. The developed algorithm provides effectively about the magnitudes of the detailed and approximate coefficients of the fault signal to characterize the fault signal. This logic can even be extended to realize system on chip by implementing FPGA technology.
REFERENCES
1. 1 A.A Girgis, M.B.Johns “A Hybrid expert system for faulted section identification, fault type classification and selection of faulted location algorithms”. IEEE Trans. Power Delivery, vol.4, No.2 April 1989
2. W. K. Yoon, M. J. Devaney, “Reactive Power Measurement Using The Wavelet Transform”, IEEE Trans. On Instrumentation & Measurements, Vol 49, No 2, April-200, pp.246-252
3. S. Mallat, “A Wavelet Tour of Signal Processing Academic Press, 1999.
4. Jeff Lamoree, Dave Mueller, Paul Vinett, William Jones, Marek Samotyj, “Voltage Sag Analysis Case Studies”, IEEE Transactions on Industry Applications, Vol. 30, No. 4, PP..1083-1089, July / August 1994.
5. S. Pastore, S. Quaia, L. Torelli, “Voltage Sag Analysis through Wavelet Transform”, IEEE. Electrotechnical Conference, 1998. MELECON 98. Vol.2. PP 959 – 963.
6. S.Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation”, IEEE, Trans. on Pattern Anal. and Mach. Intell., vol. 11, pp. 674-693, 1989.
