Multi-Resolution Wavelet Analysis for Chopped Impulse Voltage Measurements

Multi-Resolution Wavelet Analysis for Chopped Impulse Voltage Measurements EMEL ONAL Electrical Engineering Department Istanbul Technical University 34469 Maslak-Istanbul TURKEY onal@elk.itu.edu.tr http://www.elk.itu.edu.tr/~onal Abstract: - In this study, an application of the wavelet transform based on the multi-resolution analysis (MRA) is aimed for evaluation of amplitude and time parameters of the chopped impulse voltage. In terms of the getting data set, chopped lightning impulse voltages with different chopping times are considered and MRA is applied to these data as different case studies. Hence, some characteristic properties are extracted from the impulse waveforms at some special frequency values. In this sense, frequency component of 33 MHz is found with a maximum peak value for each case before the chopping time and their appearing times for two cases are determined using the time-frequency analysis. Hence difference between the chopping time and occurring time of the maximum peak values at 33 MHz is calculated easily. Also, some physical interpretations of the frequency component of 33 MHz are defined through the circuit parameters of the measurement system. In usual application, the MRA can be presented as a powerful technique to extract the noise effects, which come from the different sources, in the high voltage measurements. Keywords: - Chopped impulses, Wavelet transforms, Multi resolution analysis, High voltage, Signal energy 1 Introduction Due to the very high voltage levels involved in high voltage testing, it is necessary to use a test circuit that is able to furnish an image of the impulses used in the tests with a level suitable to be applied to the input of a digital recorder, an oscilloscope or a voltmeter. Instead of providing the desired pulse shape given in the standard, the waveform recorded produces a more or less distorted shape, depending on the equipment under test, the quality of the components of the measuring system, and on the ambient conditions at the test site. It is therefore difficult to establish traceability of the test results and compare them with those of other HV laboratories [1-3]. The three possibilities of disturbances are dominant in terms of frequency content, oscillation on the test circuit, electromagnetic disturbance and digital circuit noise. Those three types of disturbances have different frequency characteristics. The oscillations due to the test circuit rarely have frequencies above 500 khz, the electromagnetic disturbance usually is characterized by frequencies in the range of several hundreds of kilohertz (above 500 khz) up to a few megahertz (less than 10 MHz) and the noise from the digitizers most commonly used in HV test setup has frequencies clearly above 10 MHz. All the disturbances with frequencies above 500 khz must be removed from the lightning voltage waveform before the evaluation of the impulse parameters [4]. As stated above, efficient waveform processing may only be attained if good information is available about the two domains: the frequency content, the time localization and duration of the disturbances. The frequency content determines the decision whether a given frequency component corresponds to a disturbance that should be removed, or not. The time localization and duration determines the removal technique to avoid changing the undisturbed zones. Wavelet transform is a powerful signal processing tool for computing timefrequency representation of signals. The use of wavelet transform is particularly appropriate since it gives information about the signal both in frequency and time domains [5]. The implementation of the method also requires knowledge and through understanding of the noise present, which can be extremely difficult, especially for on-line monitoring of impulse activities [6-7]. Wavelet analysis is nowadays quite well known and used in many application fields, particularly where there is a need to detect and characterize small energy signals superposed to large energy signals. ISSN: 1790-5109 73 ISBN: 978-960-474-108-3

2 Experimental set-up and MRA Application to Impulse Signals The lightning impulse voltages used in this study was produced by a 280 kv, 200 J, two stages Marx type impulse generator. The chopped impulse voltages were obtained from full impulse waves chopped by a spark-over at a sphere gap parallel connected between output terminals of the impulse generator. The voltages were measured by means of a capacitive divider and recorded by Hewlett Packard 54600B digital oscilloscope having 8 bits A/D converter and taken on a computer using special software via the oscilloscope (Figure 1). Table 1. Frequency sub-bands of the noisy signal. Approximations Sub-bands (MHz) Details Sub-bands (MHz) Ca 1 0-50 Cd 1 50-100 Ca 2 0-25 Cd 2 25-50 Ca 3 0-12.5 Cd 3 12.5-25 Ca 4 0-6.25 Cd 4 6.25-12.5 Ca 5 0-3.125 Cd 5 3.125-6.25 Ca 6 0-1.5625 Cd 6 1.5625-3.125 Ca 7 0-0.78125 Cd 7 0.78125-1.5625 HV Impulse Generator Voltage Divider Measuring Cable Digital Oscilloscope Data Cable Figure 1. Experimental set-up. Personel Computer Printer S. Mallat introduced an efficient algorithm to perform the multi-resolution analysis MRA [8]. The MRA is similar to a two-channel sub-band coder in high-pass (H) and low-pass (L) filters, from which the original signal can be reconstructed. The low frequency sub-band is referred to as approximation Ca i and the high-frequency sub-band by detail Cd i. Thus, the signal may be reconstructed as S = Ca n + Cd 1 + Cd 2 + + Cd N at the N th stage. Finally, in this study, signal reconstruction at seven stage is given as S = Ca 7 + Cd 1 + Cd 2 + Cd 3 + Cd 4 + Cd 5 + Cd 6 + Cd 7. The analysis of the impulse waveform data was performed using MATLAB 5.1 Wavelet Toolbox [9]. Several steps were performed before MRA or the sub-band analysis. The frequency spectra were computed in order to establish denoising signal. These wavelet basis functions were determined to be Daubechies-20 (db-20) for noisy signal [10]. The sub-band calculation or the MRA of the signal was performed by dividing into seven sub-bands in the frequency range 0-100 MHz. The sample rate was 200 MSa/s and record length was 1000 samples for each window of the oscilloscope. All computed sub-bands are shown in Table 1 as details (Cd 1 -Cd 7 ) and approximations (Ca 1 -Ca 7 ). To be analyzed original signal (S0) can be separated to the sub-bands dividing as represented in the Table 1. Results of the related sub-band analysis, which is named as Multi-Resolution Analysis (MRA), can be given by following table for approximation and detail sub-bands. 3 Examples for Measurement of Chopped Impulse Voltage In this section, it is considered two different cases, which are denoted by Table 2, to show the various transient cases from chopped impulse voltage measurements using the experimental set-up as shown by Figure 1. These signals are shown in Fig. 2 and Fig.3 for case 1 and case 2 respectively. For each case, the Multi-Resolution Wavelet Analysis (MRA) technique is used for the transient analysis and to indicate its characteristic properties. Case Study 1: This application is due to the impulse voltage waveform chopped on the front as shown in Figure 2. Here time to chopping is at around 1.265 µs before the virtual front time T 1 = 1.437 µs. Figure 2. Impulse waveform chopped on the front for case study 1. Case Study 2: For this application, considered impulse voltage waveform chopped on the tail is ISSN: 1790-5109 74 ISBN: 978-960-474-108-3

shown by Figure 3, here time to chopping is at around 2.095 µs, which is later the virtual front time T 1 = 1.871 µs. components which are related to the transient cases of chopped impulse voltage measurements. In term of the MRA results, most characteristic frequency value occurs at 13.8 MHz as a third sub-band property and also, the second important frequency value is at the 33 MHz of the second sub-band of two different case studies. As seen from the Figure 2, the chopping time is short than the virtual front time, for this case, the MRA procedure is applied on the signal and the following results are obtained. The impulse wave form, which is indicated by Figure 2, has the frequent ripples on the main waveform. The reason of these ripples is related to high frequency components like sub-band 2 because the amplitudes of the sub-band 2 are very high in the frequency domain which is defined between the 25-50 MHz. Figure 4 shows the results of MRA of chopped impulse response for case study 1. Figure 3. Impulse waveform chopped on the tail for case study 2. Table 2. Characteristics of two different chopped waves. Characteristics Peak of the Chopped Value Impulse U max Voltages [kv] Virtual Front Time T 1 [ns] Time to Chopping T c [ns] Time base or Sweep Speed t [ns] Number of Data Points Case 1 38.50 1437.2 1265 500 1000 Case 2 34.88 1871.4 2095 500 1000 The detail sub-band 2 has minimum signal energy for our signals. This means that the sub-band 2 has the lower amplitudes in the time domain and it denotes a common property, which is defined at the same signal energy value for two different case studies of this research. If so, it can be indicated as an optimal sub-band selection of this application. But, at the same time, this sub-band has high frequency content as second detail band of the multi-resolution wavelet analysis. This feature can be extracted from Table 1 and Figure 4 easily. Also, its amplitudes appeared in the frequency domain are most dominant with huge peaks in the high frequency region of the original data. In this sense, the sub-band 2 is interpreted as an informative subband. This result shows that the second detail subband between 25-50 MHz is more informative in terms of the frequency analysis. Hence, the second detail sub-band is considered to show the frequency Figure 4. MRA of chopped impulse response for case study 1. Here, Multi-Resolution Wavelet Analysis provides a perfect signal reconstruction possibility. In this manner, the sum of the all detail sub-bands (Cd1,, Cd7) together with the last approximation subband (Ca7) shows the signal reconstruction and this summation is a term by term summation. Hence we get the original signal again by means of this signal reconstruction approach. ISSN: 1790-5109 75 ISBN: 978-960-474-108-3

Figure 5. Normalized Power Density variation for second sub-band in the case study 1. within 0.172 µs, which is defined as a difference between 1.265 and 1.093 µs, before the chopping time. By the similar way with case study 1, for case 2, the most informative sub-band is the second one. For this reason, the power spectral density function is used for detecting the frequency components of the second sub-band, because it has minimum energy level. For case 2, there are several huge peak values according to accepted certain threshold level, for example 0.4. These huge peak values appear at 27.6 MHz, 32.2 and 32.6 MHz respectively. Here the 32.2 and 32.6 MHz can be accepted as a fundamental frequency at around the 33 MHz. In case 2, it is observed that the amplitude of the frequency at 33 MHz has a maximum value in 2.423 µs according to time base origin or 1.923 µs according to virtual origin of the wave and it occurs within 0.172 µs, which is defined as a difference between 2.095 and 1.923 µs, from the chopping time. Figure 6. Time-frequency domain for second sub-band in case study 1. Figure 5 shows the Normalized Power Spectral Density (NPSD) variation, which is computed for second sub-band analysis of the MRA results using the Short-Time Fourier Transform. The result of the NPSD shows huge peak values of the frequencies, which are appeared at 27.2 MHz, 33 MHz, and 41 MHz. By means of Figure 6, it is determined appearing time of the maximum amplitude at 33 MHz and then, it can be obtained as 1.593 µs according to time base origin or 1.093 µs according to virtual origin of the wave. As a result, amplitude of the frequency at 33 MHz is a maximum value of this analysis and it occurs 4 Conclusion In this research, it is considered Multi-Resolution Wavelet Analysis (MRWA) for chopped impulse voltage measurements for two different chopped waveforms. For this purpose, the chopping times for each waveform are accepted at the different times according to their virtual front times. In this manner, sub-band analysis, which is based upon the MRWA, is realized for each case. However, before this application, the most important sub-band level is determined to extract the useful information before the chopping times through the frequency analysis. To do this, it is considered the signal energies for each detail sub-bands which are obtained from the MRWA and for each case studies, as common result, the second detail sub-band is determined as more informative sub-band in terms of the frequency analysis. Hence, spectral calculations are realized for this second detail sub-band and most indicative peak value, which appears at around the 33 MHz, is detected as a result of these analyses. In this sense, the frequency component at 33 MHz can be accepted as a joint characteristic property for each different case study. After this determination, the other important property is its time. For this purpose, it is computed time-frequency plot and then, its occurring time is easily determined. As a result of this determination, the appearing times of the maximum peak value at 33 MHz are determined as indicated in the case studies above. Also, for the chopping times for each case, appearing time for the ISSN: 1790-5109 76 ISBN: 978-960-474-108-3

33 MHz before the chopping times are calculated as 0.172 µs for case study 1, case study 2. There are the different sources of high frequency interferences on an impulse waveform. Stray capacitances and inductances of elements in the generating and measuring circuits; circulation currents or induced currents and voltages on the measuring cable shield or all of the connection as ground and high voltage connections; signals penetrating into the recording instrument via the power supply or from electromagnetic radiation can be cause the high frequency undesired signals. High voltage switching operations and discharge phenomena in the gas gap cause electromagnetic transient [11]. These transients radiate high electromagnetic fields of high frequency and cause interference to sensitive electronic equipment as oscilloscope, voltmeter and PC. Interference of the switch increases with the applied voltage to gap space and decreases with the distance from the source. Radiation has a wide band as 100 MHz, and the peaks are at 3-12-15-33 MHz. In the frequency range from 25 to 41 MHz time-frequency distributions of the highest amplitude value were observed for second detail band. For this reason, a filter can be used between the frequency range of 25 and 41 MHz. In this state, the characteristic frequencies of the chopped wave can be found correctly. Especially in the dielectric strength experiments of transformer windings this technique is applied effectively. Hence, MRWA is presented as a powerful technique to extract the hidden information based on the noise effects, which come from the test setup like spark gap, in the high voltage measurements. In this sense, features regarding sub-band 2 indicates this kind of the hidden information and having these features can be useful in terms of the calculation of the circuit parameters in the sense of the filter design. Therefore, this approach can be recommended to the other researchers for their similar studies. waveforms with oscillations and/or an overshoot, IEEE Trans. on Power Delivery, Vol. 12, No. 2, Apr. 1997, pp. 640 649. [4] L. Angrisani, P. Daponte, C. Dias and A. A. do Vale, Advanced processing techniques of highvoltage impulse test signals, IEEE Trans. on Instrumentation and Measurement, Vol. 47, No. 2, April 1998, pp. 439-445. [5] S. K. Pandey and L. Satish, Multi-resolution signal decomposition: A new tool for fault detection in power transformers during impulse tests, IEEE Trans. on Power Delivery, Vol. 13, No. 4, Oct. 1998, pp. 1194 1200. [6] C. P. Dias, A. M. Moura and A. A. Vale, Digital filtering of HV impulse tests results, 7 th International Symposium on High Voltage Engineering, Dresden, Aug. 26-30, 1991, pp. 121-124. [7] L. Satish and B. I. Gururaj, Wavelet analysis for estimation of mean-curve of impulse waveforms superimposed by noise, oscillations and overshoot, IEEE Trans. on Power Delivery, Vol. 16, No. 1, Jan. 2001, pp. 116-121. [8] S. G. Mallat, A Theory for Multi-resolution Signal Decomposition: The Wavelet Representation, IEEE Trans. on Pattern Anal. Mach. Intelligent, Vol. 11, 1989, pp. 674-693. [9] M. Misiti et al., Wavelet Toolbox for use with MATLAB, The Math Works Inc., 1996. [10] I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia PA, 1992. [11] A. Claudi, R. Malewski, Checking of digital impulse analysis systems against electromagnetic interference, Ninth Int. Symposium on High Voltage Engineering, Graz, Austria, Aug. 28- Sept. 1, 1995, Paper No.4551. References: [1] High voltage test techniques- Part I: General definitions and test requirements, International Standard IEC 60-1, 2 nd., Geneva, Switzerland, 1991. [2] Y. M. Li, J. Kuffel and W. Janischewskyj, Exponential fitting algorithms for digitally recorded high voltage impulse parameter evaluation, IEEE Trans. on Power Delivery, Vol. 8, No. 4, Oct. 1993, pp. 1727 1735. [3] F. Garnacho et al., Evaluation procedure for lightning impulse parameters in case of ISSN: 1790-5109 77 ISBN: 978-960-474-108-3