2013 Electrical Insulation Conference, Ottowa, Onterio, Canada, 2 to 5 June 2013 Construction of Finite Impulse Filter for Partial Discharge Localisation inside a Transformer Winding

M. S. Abd Rahman1, P. Rapisarda2 and P. L. Lewin1 1The Tony Davies High Voltage Laboratory, University of Southampton, SO17 1BJ, UK 2Communications, and Control, University of Southampton, SO17 1BJ, UK Email: [email protected]

Abstract- In high voltage (H.V.) plant, ageing processes can strategies [1]. Generally, timed-based preventative occur in the insulation system which are totally unavoidable and maintenance is performed periodically regardless of asset ultimately limit the operational life of the plant. Ultimately, condition which leads to higher operational costs. In order to partial discharge (PD) activity can start to occur at particular save maintenance costs, general CM practice is moving from a points within the insulation system. Operational over stressing and defects introduced during manufacture may also cause PD time-based approach to on-line based on specially condition activity and the presence of this activity if it remains untreated assessment [2,3]. Therefore, partial discharge condition will lead to the development of accelerated degradation processes monitoring for transformers and also PD source location along until eventually there may be catastrophic failure. Therefore, a transformer winding have become important research areas partial discharge condition monitoring of valuable HV plant such that aim to provide asset health information, enabling as a transformers and in particular along a transformer winding maintenance and replacement processes to be carried out is an important research area as this may ultimately provide effectively. To date, various methods of PD detection have asset health information enabling the maintenance and been proposed and discussed in the literature [3]. The proper replacement processes to be carried out effectively. Wavelet and suitable detection of real PD is an important element that multi-resolution analysis consists of a series of quadrature filter banks which are associated with a high pass and low pass filter. needs to be associated with PD measurement systems. The The process is performed in order to decompose original signals detection system needs to ensure that detection can be carried into different levels that contain different time-frequency out with high sensitivity, good noise rejection and is able to resolutions of the original waveform. Thus, the spread of signal differentiate between internal and external discharge events energy over different time/frequency ranges can be determined. [2]. There are several different sensing technologies that can The use of system identification in the frequency domain using be applied such as ultra-high frequency (UHF), acoustic and the Wavelet transform provides unique selections of the optical measurements which have been extensively particular frequency range of interest of the measured PD signals investigated [4]. Based on the assumption that the PD that have propagated inside a transformer winding. Wavelet measurement technique uses current measurement to detect decomposition levels can be combined linearly with Principal Component Analysis (PCA) and this may provide useful any PD signals flowing to earth via the bushing tap and neutral information about the location of the discharge source within the to earth connections, radio frequency current transducers winding and with further implementation using an infinite (RFCT) have been found to be an effective sensing method impulse response (IIR) filter approximation, it is possible to and have been proven to be sensitive enough for PD construct a standard filter based on the Wavelet transform and measurement of discharge currents over a frequency range of PCA that can be implemented as an automatic PD localization 10 kHz to 200 MHz. More recent research has analysed tool. information using data mining methods [5,6]. The benefit of signal processing techniques such as the Wavelet transform Keywords; partial discharge; transformer; condition monitoring; (WT) as a signal decomposition tool over different the Wavelet transform; system identification; PD location. frequency and time domain and data mining technique such as

Principal Component Analysis (PCA) used as dimensional I. INTRODUCTION reduction tool is that when combined they can represent the

distribution of energy of the captured PD pulse as a single In high voltage plant, ageing processes can occur in the point in three dimensional space. This property then may be insulation system which are totally unavoidable and ultimately used as an indicator of PD location inside a transformer limit the operational life of the plant. These processes can winding. In developing this analysis, we report on the increase the likelihood of unwanted partial discharge (PD) construction of standard finite impulse response filter (FIR) to activity inside a transformer and this activity will lead to directly perform this combined operation. The technique further ageing and degradation ultimately lead to a presented in this paper is mainly based on the linear catastrophic failure. To avoid this, regular condition combination of the wavelet decomposition filter which monitoring (CM) is generally implemented and there are consists of low pass, high pass and band pass filter for every traditional corrective and time based preventative maintenance level and the related PCA loading coefficients. Hence,

978-978-1-4673-4744-0/13/$31.00 ©2013 IEEE 30 transfer functions for the corresponding constructed filters are into two components, cA1 and cD1 by scaling function and estimated using the Yule-walk equation for an IIR filter wavelet function respectively. The cA1 is known as approximation. The theory of data mining techniques is approximation coefficient of level one is then again discussed in the next section and the experiments undertaken decomposed into a level consists of a new approximation, cA2 within the Tony Davies High Voltage Laboratory are and new detail coefficient cD2, the whole process of wavelet described in following section. Obtained results using the decomposition is shown in Fig.2. technique are presented and discussed as well as conclusions resulting from this work.

II. FUNDAMENTAL METHODS

A. Discrete Wavelet Transform

The wavelet transform is a useful mathematical tool for time- frequency domain analysis. It has been applied effectively of partial discharge analysis in high voltage plant [6]. The basis of the wavelet transform requires selection of a proper mother wavelet (ψ(m)) according to the analysed signal. There are various type of mother wavelet, such as Symlet, Meyer,

Coiflet, Morlet and Daubechies wavelet which have unique Fig. 2. Iterative wavelet decomposition process. properties and are suitable for different applications. In this paper, the Daubechies wavelet is applied due to the fact that TABLE I. WAVELET FILTERS AND THEIR MAIN INTERVALS [7]. this mother wavelet was found in the initial investigation is Decomposition Frequency Frequency Frequency domain filter able to ‘map’ the characteristics of the PD pulse and hence is level(n) (min) (max) believe to be effective in analysis of transient signal produced D1 by PD activity [1]. The wavelet plays a role of high-pass, 4 2 2 D2 band-pass and low-pass filter as shown in Fig.1. The high– · 8 4 4 2 pass filter and the low-pass filter corresponding to the wavelet D3 · · function and scaling function respectively. It is shown that the 16 8 8 4 2 approximation, A, of the original signal, S, sampled at fs = D4 · · · 500MSs-1 contains the smallest frequencies (in brown line) 32 16 16 8 4 2 Dn and the details contain highest frequencies (in red line). The · 2 2 2 2 set of whole wavelet filters for each decomposition levels is summarized in Table 1. An 0 2 2

B. Principal Component Analysis

Principal component analysis is a non-parametric statistical method that is used widely and is the most popular dimensional reduction technique for large data sets and can reveal hidden patterns inside data [1,6]. Wavelet analysis generates a distribution of (n+1) energy variables over the frequency range. As such the individual PD pulse can be represented by a vector of these ten variables (or a single point in (n+1) dimensional spaces). In this paper, just three variables are used for visualization of the features hidden in the data sets, thus, PCA was used to extract these three values that best represent the (n+1) vector. Generally, the results of

PCA analysis are used to project the actual values from the Fig. 1. Frequency domains of wavelet filters at different analysis levels. correlation matrix into different value of uncorrelated variables in principal component space, but the important The combination of the wavelet and scaling functions thing in order to determine the value of the scores is the produces a band-pass filter from decomposition level 2 principal component coefficients, also known as loadings (V). onwards. For computation, usually the discrete wavelet In order to determine these loadings, Eigen-analysis is transform is used, the process of decomposition involves an performed as follows: iterative process in which, the original signal is decomposed

31 1. The data is centered by zero mean and unity The method is applied in order to compute parameters of AR variances (standardization). model using a least-square method for frequency spectral estimation based on measurement data set ultimately used to 2. Solution of eigenvalues, λ and eigenvectors. V to the design IIR filter [9]. In this problem, the true correlation covariance matrix, C. coefficients are replaced by the unbiased correlation 3. Re-arranging the matrices, λ and V in descending coefficients computed using the inverse Fourier transform of order. specified frequency response given by:

Table 2 shows an example of PC loadings for three principal 1 components derived from measurement dataset from PD 1 activity inside a transformer winding undertaken at the Tony Davies High Voltage Laboratory, University of Southampton. Referring to the table shown, there are positive and negative Where R(i) is represent the complex frequency spectrum PCA coefficients which interpret the variables differently. produced by wavelet and PCA. Generally the correlation The negative coefficient does not cause any significant coefficients and AR parameters can be represented by: important and thus plot the result in the negative part of principal component space. 0, 1 , 2

TABLE II. EXAMPLE OF PCA LOADINGS AT DISTINCT LEVELS. Equation 2 also can be rewritten in matrix form as follows:

Decomposition PCA coefficients level α β γ 1 D1 -0.0376 0.7993 0.5695 0 D2 -0.0903 -0.0611 -0.0058 D3 -0.0019 -0.1404 0.0215 D4 0.1606 -0.5601 0.8057 where p is the order of AR model. D5 0.1005 -0.0846 -0.1155 D6 0.9727 0.1231 -0.0994 B. MA parameter estimation D7 0.0721 0.0195 -0.0122 In order to complete the ARMA model, it is necessary to D8 0.0554 0.0245 0.0059 determine the MA parameters (i.e. numerator of the filter). D9 0.0045 0.0133 0.0233 Various methods in the literature to estimate the parameters A9 0.0067 0.0222 0.0454 have been proposed [10]. The procedure utilizes the Fourier

transform of the correlation sequence and the numerator III. Autoregressive Moving-Average (ARMA) coefficients, n(z) corresponding to the additive frequency The frequency responses computed from the wavelet analysis response are computed directly from the correlation after each individual decomposition level are combined coefficients given by: linearly with PC loadings that are assumed to be unique based on the partial discharge source location inside a transformer , 3 winding due to the fact that previous research has shown that the wavelet filtering and PCA are able to define two separate clusters in 3-D principal component space [1]. These where, frequency responses can be used to extract the feature from the measurement data as a standard filter without the necessity 1 of repeating the whole procedures of wavelet and PCA. In 4 order to obtain the corresponding filter according to the spectra an ARMA technique is used for spectral estimation. The result of this approach is to obtain parameters for filters Equations (3) and (4) lead to the following relationship: based on infinite impulse response (IIR) to approximate the finite impulse wavelet filter. The parameters of an · , autoregressive (AR) model has been calculated with the aid of modified yule-walk equations (MYW) while the moving or average (MA) parameter has been computed directly from unbiased sample correlation coefficients, and the estimated · , 6 AR parameters, [8,9]. This is a simple approach but provides computational A. Modified Yule-walk equations efficiency and gives reasonable results [9]. Once, the parameters n have been computed, the complete frequency

32 response corresponding to the numerator and denominator can RFCT EMCO model 93686-5, serial model 9802-50174 which be evaluated. Hence, the MA parameters, bn, can be has a measurable frequency range from 10 kHz, to 100 MHz. determined by using spectral factorization technique to power A digital storage oscilloscope, Tektronix DPO7254 with a spectral density function of the model and least squares fit bandwidth of 2.5 GHz and sampling rate 40 Gs/s was used to [11]. display, analyse and store the obtained output signals from IV. EXPERIMENT both ends.

The experiment is based on high voltage transformer winding V. RESULTS AND DISCUSSION model BS148:1998 class 1 and 60 kV transformer bushing 60HC755 in order to simulate the PD activity using artificial Obtained results from the experiment have been analysed PD sources inside a transformer winding. The transformer has using the proposed methodology two types of windings, interleaved disc and plain disc winding remains grounded during experiments; in this case the PD A. Wavelet and PCA signal source was generated and injected into the interleaved disc winding section. The interleaved winding consists of The linear combination of wavelet filters and PCA loadings are given by: eight external terminals which internally interconnected to eight sections with two discs for every section, for replicating a real high voltage transformer, terminal one of the winding is , 2 9 7 connected to the bushing core bar while the last terminal was grounded. Artificial PD sources were used to generate impulse type signals which were then injected at each terminal , 2 9 8 of the winding via a cable. The current pulses from every section of the winding which initiated by the PD activities are measured at measurement points. The selection of , 2 9 9 measurement points is based on the assumption that signals from the PD sources are travelling in both directions towards earth point, thus, there are two external measurement points Each derived filter is unique and orthogonal to each other and located at the bushing tap to earth which is connected to is therefore similar to principal components. Figure 4 and 5 terminal 1 while the other is at the neutral to earth connection shows the example frequency spectra for the filters derived and connected at terminal 8. Figure 3 shows a schematic from (7), (8) and (9) respectively with normalized frequency diagram of the experiment to inject signals into transformer and energy spectral density for both measurement terminals; winding using a PD source which is immersed in the silicone namely, the bushing tap point and neutral to earth connection. oil. From Figure4, the filters for terminal 1 clearly demonstrated that the frequency response of the filters are not identical, nevertheless, they do have similar characteristics to each other. Comparing terminal 1 (Fig. 4) and terminal 8 (Fig. 5) for each filter A, B and C, there are significant differences in spectral properties between the two terminals.

Fig. 3. A transformer winding model to inject PD pulses into a winding section for simulating PD activity inside a winding.

Based on the previous assumption that any discharge events will induce discharge current flowing towards earth via those two points, the current flowing to the both ends is electrically measured using a radio frequency radio transducer (RFCTs). The RFCT used in this experiment is the clamp-type split core Fig. 4. Frequency spectrum plots for terminal 1.

33 signal. On the other hand, high order transfer functions introduce delay and increase the complexity of implementation. Thus, there is an optimum order of transfer function to estimate the frequency spectra and maintain accuracy whilst providing a fast filtering process.

VI. CONCLUSIONS

The Wavelet transform is a method that enables analysis of discrete signals in the time and frequency domains via a cascading decomposition process for different time-frequency resolution. Both consist of low-pass and high-pass filters and these filters can be used as a (i.e. band-pass filter). The use of PCA as a non-parametric dimension reduction technique to reduce the dataset is useful to aid visualization process and feature extraction. Previous work [1], applied both

Fig. 5. Frequency spectrum plots for terminal 8. of these methods to develop a new approach to PD localization process inside transformer winding and was B. PD localization shown promising results. Thus, this paper considers developing a standard filter based on the idea that Wavelet is The frequency spectra in Figure 4 also show indirectly the also in the form of finite impulse response filter with distinct principal components used in the PD localization approach frequency responses at different decomposition levels. The reported in [1]. The spectral estimation method discussed in ARMA model provides an approach for spectral estimation the previous section is used to derive transfer function of the and ultimately designing standard filters according to the filters. Ultimately, the results produced by the filters are used computed frequency spectrum which can be used to extract the to compute corresponding distribution of energy as shown in feature from the PD measurement data with the intention of Figure 6, where the blue and red clusters represent the bushing developing an autonomous condition monitoring technique for tap and the neutral to earth connection respectively. high voltage transformers.

REFERENCES

[1] M. S. Abd Rahman, L. Hao and P. L. Lewin, “Partial discharge location within a transformer winding using Principal Component Analysis,” 17th International Symposium on High Voltage Eng. , CD-ROM, Aug. 2011. [2] P. L. Lewin, I. O. Golosnoy and R. Mohamed, “Locating partial discharge sources in high voltage transformer windings” Electrical Insulation Conference, pp.196-200, June. 2011. a. b. [3] A. A. Elanin and M. Salama, “Survey on the transformer condition monitoring” Conference Pow. and Large Eng. Sys., pp.187-191, Montreal, 2007. [4] P. Werle, H. Borsi and E. Gockenbach,“A new method for partial discharge location on power transformers based on a system theoretical approach”, Int. Conf. on Prop. & App. of Dielectric Materials, 2000, pp.831-834. [5] R Mohamed ‘Partial Discharge Signal Propagation Modelling and

c. d. Estimation in High Voltage Transformer Windings’ PhD Thesis, Fig. 6. Plots of distribution of energy computed from the filters output. a) University of Southampton, 282 pages, Sep. 2010. terminal1 b) terminal 3 c) terminal 4 d) terminal 8. [6] L. Hao and P. L. Lewin, "Partial Discharge Source Discrimination using a Support Vector Machine", IEEE Trans. Dielectr. Electr. Insul., Vol. 17, 2010, pp. 189-197. Figure 6(a) shows the clusters of bushing tap and neutral to [7] Z. Vana, H. A. Preisig, ‘‘System identification in frequency domain earth connection are close to each other in contrast to Figure using : Conceptual remarks’’ Sys. & Cont. Letters, July, 2012. 6(b) where the clusters fall apart in significant distance in 3-D [8] W. Haijun, L. Guizhong, F. Wanchun, ‘‘A new time-frequency analysis based on AR model’’ Int. Conf. Neural Networks & Signal Processing, energy plot. Based on the plots, it is evident that the filters do Nanjing, China, Dec, 2003, pp648-651. work in order to distinctly separate the PD activity location [9] B. Friedlander and B. Porat, ‘‘The modified yule-walker method of within a transformer winding as expected. However, the ARMA spectral estimation’’, IEEE Trans. Aero. & Electronics Sys, energy plots from the current work are not the same as what March,1984, 20(2), pp158-172. [10] N. Sandgren, P. Stoica and P. Babu,‘‘on parameter produced directly from PCA as the calculated energy is always estimation’’, European Signal Processing Conference, August, 2012, positive. The results are produced by filters of order 30 and Bucharest, pp2348-2351. the accuracy is determined by the order of the transfer [11] J. A. Cadzow, ‘‘Spectral estimation: An over determined rational model functions. A low order of transfer function provides an approach’’, IEEE proceedings, Vol.70, No. 9, Sept. 1982, pp907-937. advantage of fast filtering but produces a low quality of output

34