NOISE REDUCTION OF PARTIAL DISCHARGE SIGNALS USING LINEAR PREDICTION AND WAVELET TRANSFORM

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1 NOISE REDUCTION OF PARTIAL DISCHARGE SIGNALS USING LINEAR PREDICTION AND WAVELET TRANSFORM Babak Badrzadeh and S.M.Shahrtash Department of electrical engineering Iran University of Science and Technology Tehran Iran IRAN Abstract: Partial discharges are caused by various defects such as voids, shield protrusions, contaminants, advanced stages of water tree, etc and known the main cause of breakdown in insulation materials. Partial discharge (PD) location is a powerful and useful tool for the maintenance and operation of electrical power distribution cables. This paper describes the application of two digital signal-processing techniques (Linear prediction and Discrete Wavelet Transform) to partial discharge site location. These techniques have been used for both on-line and off-line PD location. Results show the effectiveness of these algorithms and by applying them to the acquired signal one obtain almost the true shape of PD signal under noisy conditions. Key words:- Wavelet transform- linear prediction-detection and location-condition monitoring-partial discharge-cable 1. INTRODUCTION The distribution of power in industrial complexes often relies in medium voltage shielded power cable systems. Power outages due to failure of cables or their accessories during operation could cause the forced interruption of critical processes, but in the current climate of electricity de-regulation; it is not acceptable anymore due to outage cost. It is therefore important to know the state of health of the cable network (as one of the asset) in an electricity supply system. Owing to faulty manufacturing processes or, to aging after several years of service, shielded high voltage power cables may develop various defects such as electrical tree or water tree within their insulation layer [1]. If the electric stress applied is high enough, these defects may cause PD. Locating PD sites in underground power cables is a powerful and useful tool for evaluating their conditions [2-3]. The incipient defects, which can lead to failure of the cable in service, are thus located. It is also possible to identify high-risk sections of circuits in advance and to replace just the few defective meters [4]. Thus one can prioritize different problem feeders and replace or repair them in according to asset management programs [4]. As a result, The reliability of a plant can be substantially improved if potential cable failure sites could be identified and corrected after their installation. On the other hand, if a cable were being monitored, an outage had to plan because current technology requires the cable to be taken out of circuit (Off-line testing). This, of course, means outage cost, a cost, which is unnecessary if the results of health check, was fine. Electricity companies would like to be able to do the health check on-line, thus removing the outage cost. While evaluating the location of PD, one encounters two major problems; first, the significant reduction of the of reflected pulse, as it travels for a long segment of the cable and broadens (As shown later, for PD location, one should identify amplitude first and second reflection of PD pulses form far end of the cable)[5]. The reduction in the amplitude caused by attenuation often makes it very difficult to trace the reflected pulse. The distortion of the pulse worsens with the time, causing a shift of the pulse maximum. All these lead to a decline in the location accuracy [5]. The second problem is the external disturbances such as radio and TV station broadcasting, corona, PD produced by other high voltage equipment and that occur during the on-site measurement [6]. The first problem is not very serious and can be solved by appropriate selection of sensor s bandwidth [5], but the second is very important and one must suppress the noise for accurate PD Location. As yet, various methods of noise reduction have been developed and proven successful in on-line and off-line PD measurements such as correlation[1], adaptive filtering [2-3], etc. However, in these techniques, it is necessary to measure the noise prior to a measurement (Closed-loop noise reduction) thus computational time increasing dramatically [6]. For implementing on-line measurement it is necessary to

2 keep computational time as low as possible. For this purpose, Open-loop noise reduction techniques such as wavelets has been proposed [6].It is no need to determine the reference noise in theses techniques, thus reducing the computational time to lowest values. In this paper we focus on two digital filters: Linear Prediction (LPC) and Discrete Wavelet Transform (DWT). 2 NOISE REDUCTION 2.1 LINEAR PREDICTION Linear prediction is a powerful technique for predicting a signal, which is, in this study, corrupted by noise. This algorithm predicts the following sample with a certain probability by valuing the previous samples.fig.1 shows the schematic diagram of LPC for PD detection and/or location. For a signal or a class of signal (s(n)) the estimated value by linear predictor of order N is[2]: s p (n)= N i=α i s(n-i) (1) The optimum predictor is the one that minimize the mean square prediction error [2]: E= e 2 (n)=? [(s(n)-? N i=1α i s(n-i))] 2 =min (2) The coefficients of the predictor α i are to be determined from degree N so that the expected value of the prediction fault signal E goes to zero [2]: E/ α i =0 (3) This equation leads to calculation of auto-correlation function of the signal, but description of calculation procedure would get beyond the scope of this paper. Fig.1 schematic diagram of PD detection by LPC 2.2 WAVELET TRANSFORM WAVELET THEORY Fourier analysis is a mathematical tool for transforming our view of the signal from time-based to frequencybased but this technique has a serious drawback. In transforming to the frequency domain, time information is lost [7]. This drawback is very important for nonstationary signals such as PD. In an effort to correct this deficiency Gabor approved the Short-Time Fourier Transform (STFT) analysis [7]. The STFT compromise between time and frequency information, but its drawback is that once you choose a particular size for the time window, the window is the same for all frequencies. Many signals require variable window size to determine more accurately either time or frequency. To overcome the limitation of Fourier methods, the Wavelet analysis is a variable windowing technique and allows the use of long time intervals where we want more precise low-frequency information and shorter regions where we want high frequency components. For digital implementation of wavelets we use from DWT that is given by [7]: DWT(m,n)= (a 0 m ) -0.5 f(k)[ψ((n-ka 0 m )/(a 0 m ))] (4) Where ψ(k) and f(k) are wavelet function(mother wavelet) and original signal, a m 0 and ka m 0 are scaling and translation constants, respectively and k,m are integer variables. Wavelets are formed using high- and low-pass FIR filters (Fig.2)[7]. In this figure the arrows denote downsampling by 2. Outputs of these high- and low-pass-filters can mathematically be expressed by [7]: y HP [k]= u[m].g[2k-m] y LP [k]= u[m].h [2k-m] Where u denotes original signal and g, h denote high- and low-pass FIR filters, respectively. DWT permits decomposition into the sum of approximation (high-scale, low frequency components) and details (low-scale, high frequency components) elements. In other words, detail and approximation elements relate to high- and low-pass filters, respectively. The Inverse DWT (IDWT) is then used to reconstruct the signal to the original signal with no loss of information (Fig.3)[7]. In this figure the arrows denote up-sampling by 2.Outputs of high- and low-pass filters in reconstruction stage can be expressed by [7]: u[m]= {y HP (k).g[2k-m]+y LP (k).h[2k-m] (6) (5)

3 If x(t) >λ; then δ λ H =x(t) ; else δ λ H =0 (7) And the soft threshold signal is [8]: If x(t) >λ then; δ λ S =SGN(x(t)(x(t)-λ));else δ λ S =0 (8) Fig.2 Dyadic wavelet decomposition Fig.3 Dyadic wavelet reconstruction The type of wavelet used is determined by the decomposition filters. Any type of mother wavelet can be used in the wavelet analysis, but we have experimentally chosen to use db9 in all the transformations.fig.4 shows the db9 mother wavelets. Fig.4 db9 mother wavelet WAVELET DE-NOISING The general de-noising procedure involves three steps. The basic version of the procedure follows the steps described below: 1.decompose Choose a wavelet, choose a level N (2-10), and compute the wavelet decomposition of the signal at level N. 2.Threshold detail coefficients For each level from 1 to N, select a threshold and apply soft thresholding to the detail coefficients. 3.Reconstruct Compute wavelet reconstruction using the original approximation coefficients of the level N and the modified (after thresholding) detail coefficients of levels from 1 to N.Two points must be addressed: how to choose threshold, and how to perform thresholding.let λ denote threshold. The hard threshold signal is [8]: Where SGN denotes sign function. The hard procedure creates discontinuities at x=± λ, while the soft procedure dose not, as a result, it is advisable to use soft thresholding for de-noising. In this method the key is the step two: numerical choice of the threshold λ. The choice is critical, if the threshold is to small or to large. Either the result of de-noising is dissatisfied or the large distortion can be caused. There are four selection rules that are as follows [10]: rigsure : adaptive threshold selection using principle of Stein s Unbiased Risk Estimate (SURE) heursure: heuristic variant of the first option sqtwolog: universal threshold minimaxi: minimax threshold but by using these rules,the noise is not completely removed and for best performance, it would better to select the thresholds manually. 3. PD LOCATION PROCEDURE Energize the cable with an appropriate excitation voltage and increase the voltage level until a PD is detected or the maximum pre-established is reached. Reduce the voltage to zero after a very short dwell time. reader is referred to [11] for further information. 3.1 OFF-LINE PD LOCATION This is explained by means of Fig.5. Assume that PD occurs at a point C along a cable AB. The PD pulse splits into two identical pulses that travel in opposite directions. The pulse traveling left reaches the near end, A, and is recorded as the first pulse on the figure. The pulse travelling in the opposite direction is entirely reflected at point B and travels back to point A where it is recorded as the second pulse on the figure. The pulse that had reached point A first is reflected at A, then at B and returns back to A after having traveled one round trip along the cable. It is recorded on the figure as the third pulse. The unknown distance AC can be given by the following equation [11]. AC=(t 1 /t 2 ) AB (9)

4 Fig.5 Principle of PD location by reflectometry 3.2 ON-LINE PD LOCATION The principle of Reflectometry can be readily applied if both cable ends are disconnected from the system and if the cable section has no branching. The arrival time PD location method illustrated in Fig.6 can be applied even when the cable ends are not disconnected from the system and whenever the cable is branched. Capacitate or inductive sensors, installed at both ends, detect the arrival times, t 1 and t 2, of the PD pulse. Knowing the total cable length, L, and the propagation velocity, v, the location, x, of the PD site can be determined as follows [11]: x=1/2[v(t 1 -t 2 )+L] (10) are first decomposed into eight levels using db9 wavelet (Figs 11,12). In these figures a 8,d 1 -d 8 denote approximate and detail coefficients at different levels. The first five scales are omitted as they contain mostly noise, thus, wavelets coefficients are set to zero for these scales. Soft thresholding are performed on scales 6,7 and 8 since the PD pulses are prominent in those scales (We don t use from a 8 in threshoding). After soft threshing process, the signals are reconstructed using IDWT with the results as illustrated in Figs. 13,14. In these cases calculation show that the PDs are located and meters from near end of the cables. 4.2 ON-LINE PD LOCATION In this case, data are recorded from both ends of the cable (say end A, B) during in-service PD measurements of a 1.4-km, 11 kv cable [12]. The velocity of propagation and sampling rate are 168 m/µsec and 50 sample/µsec.the real PD site is located 1110 meters from near end of the cable. Fig. 15 shows the signal that recorded from end A of cable. Wavelet de-noising procedure is similar to previous and we don t repeat it. Figs. 16,17 show the de-noised signals of end A and end B of the cable, respectively. By applying (10) to these signals,pd location has been determined meters from near end of the cable. Fig.6 Principle of PD location by arrival time method 4. SIMULATION RESULTS 4.1. OFF-LINE PD LOCATION In this case, PD signals are recorded from 6 and 10 kv cables [1]. Figs.7, 8 show these signals respectively. Both cables have the length of 600 meters. The real PDs are located 160 and 110 meters from near end of the 10 and 6kV cables, respectively. We first apply LPC technique to extract actual PD signals from these raw signals. Figs.9, 10 show de-noised signals. For the best performance of LPC, the prediction order (N) is set experimentally to 34. According to Figs.9, 10 and by using (9), PD locations can be determined and meters from near end of 10,6 kv cables, respectively.in wavelet de-noising method, the signals Fig.7 PD signal from 10 kv cable Without LPC filtering Fig.8 PD signal from 6 kvcable Without LPC filtering

5 Fig.9 PD signal from 10 kv cable With LPC filtering Fig.13 PD signal from 10 kv cable Fig.10 PD signal from 6 kvcable With LPC filtering Fig.14 PD signal from 6 kv cable Fig.11 Decomposition of PD signal of Fig.7 into Eight levels Fig.15. PD signal of end A of a 11 kv cable Without wavelet de-noising Fig.12 Decomposition of PD signal of Fig.8 into Eight levels Fig.16. PD signal of end A of a 11 kv cable

6 dielectric power cable and implications thereof for PD location, IEEE Electrical Insulation Magazine, Vol.12, No.1, pp.9-16, Jan/Feb Fig.17. PD signal of end B of a 11 kv cable 6. CONCLUSION This paper has presented two methods for PD location in cable networks. In off-line PD location, PDs has located by TDR principle (One end measurement) and noise suppressed by LPC and DWT. Results show the effectiveness of both algorithms, while in on-line PD location, PDs located by arrival time (Two end measurement) method and results shoe the effectiveness of DWT noise suppression (LPC isn t an effective technique in on-line PD location). 7. REFERENCES [1] R.Villefrance, Mobile system for assessment of AC high voltage cables, Ph.D. thesis, Technical University of Denmark, Feb [2] H.Borsi, Digital location of partial discharges in HV cables, IEEE Trans. On Electrical Insulation, Vol.27, No.1, pp.28-36, Feb [3] H.N.Bidhendi, Q.Su, Partial discharge location on power cables using linear prediction IEEE 5 th International Conference on Properties and Applications of Dielectric Materials, Seoul, Korea, May [6] I.Shim, J.J.Soraghan, W.H.Siew, Digital signal processing applied to the detection of partial discharge: An Overview, IEEE Electrical Insulation Magazine, Vol.16, No.3, pp.6-12, May/June [7] Wavelet toolbox for using with MATLAB, MATWORKS inc., [8] I.Shim, J.J.Soraghan, W.H.Siew, Detection of PD utilizing digital signal processing methods, part3: open loop noise reduction IEEE Electrical Insulation Magazine, Vol.17, No.1, pp6-13, Jan/Feb [9] I.Shim, J.J.Soraghan, W.H.Siew, F.McPherson, K.Sludden, Robust partial discharge measurement in MV cable networks using discrete wavelet transform IEEE Power Engineering Society Winter meeting, pp , [10] W.Xiaorang, G.Zungjun, S.Yong, Y.Zhang, Extraction of partial discharge pulse via wavelet shrinkage, IEEE 6 th International Conference on Properties and Applications of Dielectric Materials, China, pp , June [11] M.S.Mashikian, Partial discharge site location, selected topics, ICC Meeting, Fall [12] I.Shim, J.J.Soraghan, W.H.Siew, Partial discharge location on high voltage cables, IEE High Voltage Engineering Symposium, August [4] C.M.Walton, Detecting and locating MV failure before it occurs, Experience with live line partial discharge detection on underground paper insulated 11kv cables in London, IEE CIRED.2001 Conference, June [5] S.Boggs, A.Pathak, P.Walker, Partial discharge XXII: High frequency attenuation in shielded solid