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0 IEE 2002 Electronics Letters Online No: 20020223 DOI: 10.1049/el:20020223
E-mail: jaelee@ajou.ac.kr References
26 November 2001
Jae-Chon Lee (Department o Systems Engineering, Ajou Universig, f 5 Won-Chon-Dong, Pal-Dal-Gu. Su- Won-Si, 442-749, Korea)
‘An adaptive RAM-DFE for storage channels’, IEEE Truns. Commun., 1991,39, pp. 1559-1568 2 WIDROW, B., MCCOOL, J., and BALL, M.: ‘The complex LMS algorithm’, Proc. IEEE, 1975,63, pp. 719-720 3 CHERUBINI, G.: ’Nonlinear self-training adaptive equalization for partialresponse systems’,IEEE Trans. Commun., 1994, 42, pp. 367-376 4 COWAN, C.F.N., SMITH, S.G., and ELLIOT, J.H.: ‘A digital adaptive filter Using a memory-accumulator architecture: theory and realisation’, IEEE Trans. Acoust.. Speech Signal Process., 1983, 31, pp. 541-549
f=Z+I,
f’=-I+I,
Introduction: In the design of a protection relay for large power transformers, the second harmonic of the current signal has been frequently utilised as the characteristic component of the asymmetrical magnetisation peculiar to the inrush to block the trip signal triggered by magnetising inrush conditions [ 11. However, for modern power transformers the second-harmonic contents of inrush currents may drop below 7% whereas the fault current may be more than 15%, and certain difficulties arise when protecting such transformers by using harmonic analysis-based algorithms. In this Letter we introduce a mathematical morphology-based algorithm [2] to identify transformer magnetising inrush current in the time domain. Identification method: To morphologically decompose a signal f as f; with a set of components {h,= 1, 2, . . . }, a constructive i transform can be applied to obtain a family of residues of $ If the residue of two transforms, 4 and $, is defined as R { 4 , i t ( f ) 4(f) $(f ), with an antiextensive and positively = defined transform y , the general representation scheme [3, 41 can be defined as: the family of residues offwith respect to y is {ri, i= 1, 2, . . . }, where r l =f and r;+, =R{7,,y(r,)) y(rJ is a null signal; the until set Cr;}, f ; = y(rJ is the residual representation off with respect to constructive transform y . The reconstructionf* offcan be obtained as f*= J;. The partial j-components reconstruction is given by
A novel method based on morphological signal decomposition, to
identify the power transformermagnetising inrush current waveform is
presented.
To perform the decomposition, the input current waveform is firstly transformed to obtain two signals f and f ’ , defined as
for a large N compared to that of N M for the direct form. As an altemative, the N-table realisation was also presented with reduction in multiplication counts. However, the single table structure benefits from N locations update at a time, resulting in a lot faster convergence. Exploiting some symmetry in the signal constellation and the segment-reassemble concept used in the work on distributed arithmetic [3, 41, an extension of this work to the case of general input quantised with eight bits or more would be a subject of further study.
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1010
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1015
1020
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1 FISHER, K.D., CIOFFI, J.M., ABBOTT, WL., BEDNARZ, PS., and MELAS,
C.M.:
Fig. 1 Typical inrush current waveform Consider a typical cycle of the inrush current as shown in Fig. 1, where the 50 Hz current signal I is normalised as I/In. The asymmetries of the waveform exhibit in both amplitude and duration of the positive and negative segments. If the signal is decomposed to obtain amplitudes of peak A,,, and valley A,,,, from a flat support of given length L, then the asymmetries of the amplitude and interval S between them can be quantified and compared with those in the internal fault current and normal power system operation conditions. The morphological system for identifying the magnetising inrush current is shown in Fig. 2.
Morphological identification of transformer magnetising inrush current
Fig. 2 Block diagram of proposed method
P. Sun, J.F. Zhang, D.J. Zhang, Q.H. Wu and S. Potts
,f=
xi
where Io is a predetermined constant. lo is necessary since the morphological decomposition requires that the input signal f satisfies If0 kg](t)> 0. The value of Io is not important as long as it results in bothfandf‘ being positive. Since the current signal contains both peaks and valleys, due to the erosion operation in the decomposition procedure being able to only extract peaks of a signal, the inverted input signalf’ is decomposed separately and then inverted again to obtain the valleys of the signal. The structuring function g involved for decomposition is a simple zero-valued flat line with 0.002 s length, with its origin at the centre. However, the maximum number of iterations of decomposition does not have to be as large as to obtain a full reconstruction of the original signal, as long as it can extract the peaks of the waveform for measurement. In our study, we choose 0.008 s as the final structuring function. Therefore, there are three iterations of morphological transform, with structuring function length at 0.002, 0.004, 0.006, 0.008, respectively, and accordingly the output signal in either positive or negative segment is the sum of r 2 , r 3 , r4 and r 5 . Simple criteria can be employed to quantify the asymmetry in a signal, as follows:
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