• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.21 no.4
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• pp.348-353
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• 2008

Most of the high voltage insulation systems, such as the power cable joint having hetero interface, are composed of more than two different insulators to improve insulating performance. The partial discharge(PD) in these hetero interface is expected to affect the total insulation performance. Thus, it is important to study electrical properties on these interfaces. This study described the influence of copper and semiconductive substance defects on $\Phi$-q-n distribution between the interface of the model cable joints to classify PD source. PD was sequentially detected for 600 cycles of the applied voltage. The K-means cluster analysis has been analyzed to investigate the $\Phi$-q-n distribution. The skewness-kurtosis(Sk-Ku) plot from K-means clustering results was defined to quantify cluster distribution and classify distribution patterns. The Sk-Ku plot is composed of skewness and kurtosis along abscissa and ordinate which indicate the asymmetry and the sharpness of distribution. As a result of the Sk-Ku plot, it was confirmed that the data was distributed in 1st 2nd and 3rd quadrant at copper foreign substance defect, but in case of semiconductive foreign substance, the data was distributed in 2nd quadrant only.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.25 no.3
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• pp.229-235
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• 2012

This paper dealt with the fabrication of a partial discharge (PD) analyzer for insulation diagnosis of power facilities like transformers, cables and gas-insulated switchgears. An analytic algorithm for the phase (${\phi}$), the magnitude (q), and the pulse count (n) of PD pulse was designed and a time-frequency (TF) map algorithm was applied in the system to eliminate noises by analyzing the time and the frequency component of signals. All the algorithms were operated by a LabView graphical program. The detection circuit consists of a coupling capacitor, a detection impedance, and a low noise amplifier. A plane-plane and a point-plane electrode system were fabricated to simulate different types of insulation defects. In the experiment, we could easily understand the characteristics of PD pulses using the prototype PD analyzer.

• Proceedings of the KIEE Conference
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• 2000.07c
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• pp.1853-1855
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• 2000

An experimental investigation has been performed in order to understand the $\Phi$-q-n characteristics related to the PD taking place from the various size of artificial defects inserted in epoxy insulation. In this purpose, PD has been detected simultaneously by two different methods such as commercialized PD detector(TE571) and our detection system using self designed CT type sensor. Under the presence of void in epoxy insulation, PD has been initiated at the voltages between 16kV and 20kV which are much lower than the dielectric strength of epoxy insulation (130kV/mm$\sim$l50kV/mm). And also it is revealed that $\Phi$-q-n characteristics have been observed to be dependent upon the size of the artificial defects. Throughout this work, the on site applicability of the self designed Sensor has also been proved by comparing the results with those from the commercialized PD detector. And more one, considerable basic data regarding the insulation, diagnosis could be provided to understand the presence of the voids possibly inserted into the epoxy insulation system of the power apparatus.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.283-291
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• 2009

We investigate the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+g_1(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}),\\{\eta}_t=-L{\eta}+g_2(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}).\end{array}$$ We show the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system when the nonlinearity $g^{\prime}_1,\;g^{\prime}_2$ are bounded and $3g^{\prime}_1(-{\infty})+g^{\prime}_2(-{\infty})<{\lambda}_1,\;{\lambda}_n<3g^{\prime}_1(+{\infty})+g^{\prime}_2(+{\infty})<{\lambda}_{n+1}$.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.553-564
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• 2008

We have a concern with the existence of solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+{\mu}g(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,2{\pi}),\\{\eta}_t=-L{\eta}+{\nu}g(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,2{\pi})\end{array}.$$ We prove the uniqueness theorem when the nonlinearity does not cross eigenvalues. We also investigate multiple solutions (${\xi}(x,t),\;{\eta}(x,t)$) for perturbations of the parabolic system with Dirichlet boundary condition when the nonlinearity f' is bounded and $f^{\prime}(-{\infty})<{\lambda}_1,{\lambda}_n<(3{\mu}+{\nu})f^{\prime}(+{\infty})<{\lambda}_{n+1}$.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1211-1220
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• 2009

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian $({\phi}_p(u'))'$(t)+q(t)f(t,u(t),u'(t))=0, t $\in$ (0, 1), subject to the boundary conditions: $u(0)=\sum\limits_{i=1}^{n-2}{\alpha}_iu({\xi}_i),\;u(1)=\sum\limits_{i=1}^{n-2}{\beta}_iu({\xi}_i)$ where $\phi_p$(s) = $|s|^{n-2}s$, p > 1, $\xi_i$ $\in$ (0, 1) with 0 < $\xi_1$ < $\xi_2$ < $\cdots$ < $\xi{n-2}$ < 1 and ${\alpha}_i,\beta_i{\in}[0,1)$, 0< $\sum{\array}{{n=2}\\{i=1}}{\alpha}_i,\sum{\array}{{n=2}\\{i=1}}{\beta}_i$<1. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.401-416
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• 1994

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$ (BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega, $$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$ Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x), $$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on $\partial\Omega$.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.49 no.1
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• pp.19-23
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• 2000

Partial discharges(PD)in air insulated electric power apparatus often lead to deterioration of solid insulation by electron bombardments and electrochemical reaction. The PD caused to reduce the life time of power apparatus and to increase power losses. Thus understanding and classification of PD patterns in air are very important to discern sources of PD. In this paper, PD in air by using statistical methods was investigated. We classified air discharges, corona, surface discharges and cavity discharges by Kohonen network. For classification of PD patterns, we used statistical operators and parameters such as skewness$(S^+,\; S^-),\; kurtosis(K^+, K^-),\; mean phase(AP^+, AP^-)$, cross-correlation factor(CC) and asymmetry derived from the mean pulse-height phase distribution$(H_{avg}(\phi))$, the max pulse-height phase distribution $(H_{qmax}(\phi))$, the pulse count phase distribution $(H_n(\phi))$ and the pulse height vs. Repetition rate $(H_q(n))$.

• Journal of Korea Society of Digital Industry and Information Management
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• v.14 no.4
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• pp.9-16
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• 2018

This study described partial discharge(PD) distribution analysis between the XLPE(Cross-Linked PolyEthylene)and EPDM(Ethylene Propylene Diene Monomer) interface with unsupervised classification. The ${\phi}-q-n$ patterns were analyzed using phase resolved partial discharge(PRPD). K-means cluster analysis forms a cluster based on similarities and distances among scattered individuals, and analyzes the characteristics of the formed clusters, dividing the multivariate data into several groups according to the similarity of each characteristic, Is a statistical analysis that makes it easier to navigate. It was confirmed that the phase angle of the cluster with the maximum discharge charge was concentrated around $0^{\circ}$ and $180^{\circ}$ at 30 kV after the initial phase distribution localized around $90^{\circ}$ and $300^{\circ}$ expanded to the whole phase angle according to the voltage rise. The Euclidean distance between the center of gravity and the discharge charge in the ${\Phi}-q$ cluster increased with increasing applied voltage.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.8 no.2
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• pp.47-60
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• 1975

For the calculation of population parameter and estimation of recruitment of a fish population, an application of multiple regression method was used with some statistical inferences. Then, the differences between the calculated values and the true parameters were discussed. In addition, this method criticized by applying it to the statistical data of a population of bigeye tuna, Thunnus obesus of the Indian Ocean. The method was also applied to the available data of a population of Pacific saury, Cololabis saira, to estimate its recuitments. A stock at t year and t+1 year is, $N_{0,\;t+1}=N_{0,\;t}(1-m_t)-C_t+R_{t+1}$ where $N_0$ is the initial number of fish in a given year; C, number o: fish caught; R, number of recruitment; and M, rate of natural mortality. The foregoing equation is $$\phi_{t+1}=\frac{(1-\varrho^{-z}{t+1})Z_t}{(1-\varrho^{-z}t)Z_{t+1}}-\frac{1-\varrho^{-z}t+1}{Z_{t+1}}\phi_t-a'\frac{1-\varrho^{-z}t+1}{Z_{t+1}}C_t+a'\frac{1-\varrho^{-z}t+1}{Z_{t+1}}R_{t+1}......(1)$$ where $\phi$ is CPUE; a', CPUE $(\phi)$ to average stock $(\bar{N})$ in number; Z, total mortality coefficient; and M, natural mortality coefficient. In the equation (1) , the term $(1-\varrho^{-z}t+1)/Z_{t+1}$s almost constant to the variation of effort (X) there fore coefficients $\phi$ and $C_t$, can be calculated, when R is a constant, by applying the method of multiple regression, where $\phi_{t+1}$ is a dependent variable; $\phi_t$ and $C_t$ are independent variables. The values of Mand a' are calculated from the coefficients of $\phi_t$ and $C_t$; and total mortality coefficient (Z), where Z is a'X+M. By substituting M, a', $Z_t$, and $Z_{t+1}$ to the equation (1) recruitment $(R_{t+1})$ can be calculated. In this precess $\phi$ can be substituted by index of stock in number (N'). This operational procedures of the method of multiple regression can be applicable to the data which satisfy the above assumptions, even though the data were collected from any chosen year with similar recruitments, though it were not collected from the consecutive years. Under the condition of varying effort the data with such variation can be treated effectively by this method. The calculated values of M and a' include some deviation from the population parameters. Therefore, the estimated recruitment (R) is a relative value instead of all absolute one. This method of multiple regression is also applicable to the stock density and yield in weight instead of in number. For the data of the bigeye tuna of the Indian Ocean, the values of estimated recruitment (R) calculated from the parameter which is obtained by the present multiple regression method is proportional with an identical fluctuation pattern to the values of those derived from the parameters M and a', which were calculated by Suda (1970) for the same data. Estimated recruitments of Pacific saury of the eastern coast of Korea were calculated by the present multiple regression method. Not only spring recruitment $(1965\~1974)$ but also fall recruitment $(1964\~1973)$ was found to fluctuate in accordance with the fluctuations of stock densities (CPUE) of the same spring and fall, respectively.