• 대한수학회지
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• 제61권2호
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• pp.377-393
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• 2024

In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in ℤ^d. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.

• Kyungpook Mathematical Journal
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• 제47권4호
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• pp.529-548
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• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• Transactions on Electrical and Electronic Materials
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• 제15권4호
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• pp.182-188
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• 2014

When the windowed DFT algorithm is applied in harmonic measurements, the problem of initial-phase sensitivity will be encountered, this has an effect on harmonic amplitude accuracy. In this paper, the origin of initial-phase sensitivity is analyzed and the main factors that influence the level of initial-phase sensitivity are demonstrated. A method of reducing initial-phase sensitivity is proposed to increase the stability of harmonic measurements. We found that initial-phase sensitivity is determined by the side lobe peak level of the window functions when synchronous deviation is fixed. In addition, increasing the length of the time recorded can be used to remove initial-phase sensitivity. The correctness and validity of our conclusions have been confirmed through numerical results and field tests.

• Journal of Power Electronics
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• 제17권4호
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• pp.983-990
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• 2017

This paper proposes a model predictive control based on the discrete Lyapunov function to improve the performance of power electronic converters. The proposed control technique, based on the finite control set model predictive control (FCS-MPC), defines a cost function for the control law which is determined under the Lyapunov stability theorem with a control error compensation. The steady state and dynamic performance of the proposed control strategy has been tested under a single phase AC/DC voltage source rectifier (S-VSR). Experimental results demonstrate that the proposed control strategy not only offers global stability and good robustness but also leads to a high quality sinusoidal current with a reasonably low total harmonic distortion (THD) and a fast dynamic response under linear loads.

• 전력전자학회논문지
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• 제15권4호
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• pp.266-273
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• 2010

태양광 인버터(PCS)는 태양전지에서 발생된 전력을 계통에 연계시키는 장치이다. IEEE 1547 규격에 따르면 PCS에서 발생되는 고조파왜곡은 5% 이내여야만 한다. 일반적으로 PCS에서 계통으로 유입되는 고조파 검출은 전용 계측장치에 의해서 측정된다. 초기에 규격에 맞게 설계된 PCS의 고조파가 소자들의 노화나 제어기 고장에 의해 증가하게 될 경우 발전을 중지하거나 경보를 발생시켜야 한다. 기존의 상용화된 시스템에는 이러한 기능이 존재하지 않는다. 본 연구에서는 PCS 내부에 고조파왜곡을 실시간으로 측정하는 알고리즘을 내장시키는 방법에 대해 연구한다. 고성능 32-bit 부동소수점 DSP를 이용한 PCS를 제작하고 256-point DFT(Discrete Fourier Transform) 알고리즘을 이용하여 1[ms] 이내에 하모닉 계수를 계산하였다. 제어기 제작에 대한 설명과 실험 결과로서 연구의 타당성을 입증하였다.

• Journal of Power Electronics
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• 제18권6호
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• pp.1889-1900
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• 2018

Harmonic current mitigation is vital in power distribution networks owing to the inflow of nonlinear loads, distributed generation, and renewable energy sources. The active power filter (APF) is the current electrical equipment that can dynamically compensate for harmonic distortion and eliminate asymmetrical loads. The compensation performance of an APF largely depends on the control strategy applied to the voltage source inverter (VSI). Model predictive control (MPC) has been demonstrated to be one of the effective control approaches to providing fast dynamic responses. This approach covers different types of power converters due to its several advantages, such as flexible control scheme and simple inclusion of nonlinearities and constraints within the controller design. In this study, a finite control set-MPC technique is proposed for the control of VSIs. Unlike conventional control methods, the proposed technique uses a discrete time model of the shunt APF to predict the future behavior of harmonic currents and determine the cost function so as to optimize current errors through the selection of appropriate switching states. The viability of this strategy in terms of harmonic mitigation is verified in MATLAB/Simulink. Experimental results show that MPC performs well in terms of reduced total harmonic distortion and is effective in APFs.

• Structural Engineering and Mechanics
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• 제17권1호
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• pp.1-14
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• 2004

Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.

• 한국전산구조공학회논문집
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• 제34권4호
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• pp.221-230
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• 2021

전역 최적화 문제의 해를 유전 알고리즘을 사용하여 얻어 완전파형역산을 수행하고 층상 반무한체의 물성치를 추정하는 기법을 제안한다. 조화 수직 하중이 작용하는 층상 반무한체의 동적 응답을 측정하고, 이를 추정 물성치를 사용하여 계산된 응답과 비교한다. 응답의 추정치는 mid-point integrated finite element와 perfectly matched discrete layer를 사용하여 구성된 thin-layer model로부터 얻는다. 전역 최적화 문제의 목적 함수는 응답의 관측치와 추정치의 차이에 대한 L2-norm으로 계산된다. 유전 알고리즘을 사용하여 전역 최적화 문제의 해를 구하여 완전파형역산을 수행한다. 제안된 기법을 기본 진동 모드 뿐만이 아니라 고차 진동 모드도 우세한 다양한 층상 반무한 매질에 적용하여, 측정치가 잡음을 포함하지 않는 경우와 포함하는 경우 모두에 대해서 제안된 완전파형역산 기법은 층상 반무한체의 재료 특성을 추정하는데 적합함을 확인할 수 있다.

• 대한전자공학회논문지
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• 제8권3호
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• pp.1-14
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• 1971

본논문은 릴레이 제어기구의 안정도해석과 종합성능판별의 기초가 되는 리미트사이클진동의 주기해를 정확하고도 신속하게 얻을 수 있는 방법을 개발한 것으로서 특히 궤적법은 동종의 릴레이에 대해서는 특서정수의 변화에 대해서 직각대응시킬 수 있고, 주기해를 정확하게, 그리고 신속하게 직속할 수 있는 장점을 지닌다. 이제까지 다루워 왔던 describing 함수해석법과도 비교하여 그의 부정확성과 불편성 동종릴레이 특성정수변화에 대한 비적응성도 검토하여 궤적법의 우월을 명시하였다.

• 전력전자학회논문지
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• 제4권4호
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• pp.368-376
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• 1999

본 논문은, 대표적인 FACTS기기중의 하나인 싸이리스터제어 병렬보상기의 특성 연구를 수행한다. 이를 위하여 푸리에 공간에서 전력조류 조건을 만족하는 싸이리스터 점호각을 수치해석적으로 구하고, 그 계산 결과를 이용하여 정상상태 및 고조파 특성을 해석하였다. 그리고, Poincare Mapping 이론을 이용한 스위칭 주파수영역에서 안정도 해석과 EMTP 시뮬레이션을 이용한 시평면상에서 해석결과의 검증 및 여러 운전점에서 과도응답특성의 비교연구를 수행하였다.