• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.19 no.2
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• pp.162-168
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• 2006

Recently, diagnosis techniques have been investigated to detect a Partial Discharge associated with a dielectric material defect in a high voltage electrical apparatus, However, the properties of detection technique of Partial Discharge aren't completely understood because the physical process of Partial Discharge. Therefore, this paper analyzes the process on surface discharge of polymer insulator using wavelet transform. Wavelet transform provides a direct quantitative measure of spectral content in the time~frequency domain. As it is important to develop a non-contact method for detecting the kaolin contamination degree, this research analyzes the electromagnetic waves emitted from Partial Discharge using wavelet transform. This result experimentally shows the process of Partial Discharge as a two-dimensional distribution in the time-frequency domain. Feature extraction parameter namely, maximum and average of wavelet coefficients values, wavelet coefficients value at the point of $95\%$ in a histogram and number of maximum wavelet coefficient have used electromagnetic wave signals as input signals in the preprocessing process of neural networks in order to identify kaolin contamination rates. As result, root sum square error was produced by the test with a learning of neural networks obtained 0.00828.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.05c
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• pp.170-176
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• 2002

In this papers, we proposed the feature extraction method due to partial discharge type of transformers. For wavelet transform, Daubechie's filter is used, we can obtain wavelet coefficients which is used to extract feature of statistical parameters (maximum value, average value, dispersion, skewness, kurtosis) about acoustic emission signal generated from each partial discharge type. The defects which could occur in a transformer were simulated by using needle-plane electrode, IEC electrode and Void electrode. Also, these coefficients are used to identify signal of partial discharge type electrode fault in transformer. As a result, from compare of acoustic emission amplitude and acoustic average value, we are obtained results of IEC electrode> Void electrode> Needle-Plane electrode. otherwise, In case of skewness and kurtosis, we are obtained results of Needle-Plane electrode electrode> Void electrode> IEC electrode.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1407-1433
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• 2020

Parts I-IV showed that the number of ways to place q nonattacking queens or similar chess pieces on an n × n chessboard is a quasipolynomial function of n whose coefficients are essentially polynomials in q. For partial queens, which have a subset of the queen's moves, we proved complete formulas for these counting quasipolynomials for small numbers of pieces and other formulas for high-order coefficients of the general counting quasipolynomials. We found some upper and lower bounds for the periods of those quasipolynomials by calculating explicit denominators of vertices of the inside-out polytope. Here we discover more about the counting quasipolynomials for partial queens, both familiar and strange, and the nightrider and its subpieces, and we compare our results to the empirical formulas found by Kotššovec. We prove some of Kotššovec's formulas and conjectures about the quasipolynomials and their high-order coefficients, and in some instances go beyond them.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.31-48
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• 2007

The paper deals with the solution of some fractional partial differential equations obtained by substituting modified Riemann-Liouville derivatives for the customary derivatives. This derivative is introduced to avoid using the so-called Caputo fractional derivative which, at the extreme, says that, if you want to get the first derivative of a function you must before have at hand its second derivative. Firstly, one gives a brief background on the fractional Taylor series of nondifferentiable functions and its consequence on the derivative chain rule. Then one considers linear fractional partial differential equations with constant coefficients, and one shows how, in some instances, one can obtain their solutions on bypassing the use of Fourier transform and/or Laplace transform. Later one develops a Lagrange method via characteristics for some linear fractional differential equations with nonconstant coefficients, and involving fractional derivatives of only one order. The key is the fractional Taylor series of non differentiable function $f(x+h)=E_{\alpha}(h^{\alpha}{D_x^{\alpha})f(x)$.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.239-255
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• 2014

We develop a set of identities for Euler type sums. In particular we investigate products of shifted harmonic numbers of order two and reciprocal binomial coefficients.

• Journal of Electrical Engineering and Technology
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• v.10 no.4
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• pp.1752-1758
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• 2015

This paper presents partial discharge localization in stator winding of generators using multi-conductor transmission line (MTL) and RLC ladder network models. The high-voltage (HV) winding of a 6kV/250kW generator has been modeled by MATLAB software. The simulation results of the MTL and the RLC ladder network models have been evaluated with the measurements results in the frequency domain by applying of the Pearson’s correlation coefficients. Two PD generated calibrator signals in kHz and MHz frequency range were injected into different points of generator winding and the signals simulated/measured at the both ends of the winding. For partial discharge localization in stator winding of generators is necessary to calculate the frequency spectrum of the PD current signals and then estimate the poles of the system from the calculated frequency spectrum. Finally, the location of PD can be estimated. This theory applied for the above generator and the simulation/measured results show the good correlation for PD Location for RLC ladder network and MTL models in the frequency range of kHz (10kHz<f<1MHz) and MHz (1MHz<f<5MHz) respectively.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07b
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• pp.894-899
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• 2002

In this papers, we proposed the new method in order to diagnosis partial discharge type of transformers. For wavelet transform, Daubechies filter is used, we can obtain wavelet coefficients which is used to extract feature of statistical parameters (maximum value, average value, dispersion, skewness, kurtosis) about high frequency current signal per 3-electrode type (needle-plane electrode, IEC electrode and Void electrode.). Also. these coefficients are used to identify Signal of internal partial discharge in transformer. As a result. from compare of high frequency current signal amplitude and average value. we are obtained results of IEC electrode> Void electrode> Needle-Plane electrode. otherwise. In case of skewness and kurtosis, we are obtained results of Void electrode> IEC electrode > Needle-Plane electrode. As Improved method in order to diagnosis partial discharge type of transformers, we use neural network.

• The Journal of Information Technology
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• v.6 no.1
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• pp.65-70
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• 2003

In this papers, we proposed the new method in order to diagnosis partial discharge type of transformers. For wavelet transform, Daubechie's filter is used,, we can obtain wavelet coefficients which is used to extract featrue of statistical parameters(maximum value, average value, dispersion, skewness, kurtosis) about high frequency current signal per 3-electrode type(needle-plane electrode, IEC electrode and Void electrode). Also, these coefficients are used to identify signal of internal partial discharge in transformer. As a result, from compare of high frequency current signal amplitude and average value, we are obtained results of IEC electrode> Void electrode> Needle-Plane electrode. Otherwise, in case of skewness and kurtosis, we are obtained results of Void electrode> IEC electrode> Needle-Plane electrode. As improved method in order to diagnosis partial discharge type of transformers, we use neural network.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.3
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• pp.323-329
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• 2017

In this paper, by rigorous calculations, we consider $L^2({\mathbb{R}})-spectrum$ of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that $L^2({\mathbb{R}})-spectrum$ of the linear operator is determined by the eigenvalues of Floquet matrix.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.