• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제24권1호
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• pp.85-91
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• 2020

In this parer we express the sufficient conditions under which it is proved that a J-normal irreduciable Hessenberg matrix is tridiagonal and it is also proved that a similar statement exists for J-conjugate normal matrices

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.403-426
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• 1998

We present an algorithm to find an approximation for the stationary distribution for the general ergodic spatially-inhomogeneous block-partitioned upper Hessenberg form. Our approximation makes use of an associated upper block-Hessenberg matrix which is spa-tially homogeneous except for a finite number of blocks. We treat the MAP/G/1 retrial queue and the retrial queue with two types of customer as specific instances and give some numerical examples. The numerical results suggest that our method is superior to the ordinary finite-truncation method.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 추계학술대회 논문집 학회본부 C
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• pp.1033-1036
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• 1998

In this research project, two aspects of small signal stability are studied: improvement in Hessenberg method to compute the dominant electromechanical oscillation modes and siting FACTS devices to damp the low frequency oscillation. Fourier transform of transient stability simulation results identifies the frequencies of the dominant oscillation modes accurately. Inverse transformation of the state matrix with complex shift equal to the angular speed determined by Fourier transform enhances the ability of Hessenberg method to compute the dominant modes with good selectivity and small size of Hessenberg matrix. Any specified convergence tolerance is achieved using the iterative scheme of Hessenberg method. Siting FACTS devices such as SVC, STACOM, TCSC, TCPR and UPFC has been studied using the eigen-sensitivity theory of augmented matrix. Application results of the improved Hessenberg method and eigen-sensitivity to New England 10-machine 39-bus and KEPCO systems are presented.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 추계학술대회 논문집 학회본부 B
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• pp.685-688
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• 1998

In this research project, two aspects of small signal stability are studied: improvement in Hessenberg method to compute the dominant electromechanical oscillation modes and siting FACTS devices to damp the low frequency oscillation. Fourier transform of transient stability simulation results identifies the frequencies of the dominant oscillation modes accurately. Inverse transformation of the state matrix with complex shift equal to the angular speed determined by Fourier transform enhances the ability of Hessenberg method to compute the dominant modes with good selectivity and small size of Hessenberg matrix. Any specified convergence tolerance is achieved using the iterative scheme of Hessenberg method. Siting FACTS devices such as SVC, STACOM, TCSC, TCPR and UPFC has been studied using the eigen-sensitivity theory of augmented matrix. Application results of the improved Hessenberg method and eigen-sensitivity to New England 10-machine 39-bus and KEPCO systems are presented.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 추계학술대회 논문집 학회본부A
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• pp.365-368
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• 1998

In this research project two aspects of small signal stability are studied: improvement in Hessenberg method to compute the dominant electromechanical oscillation modes and siting FACTS devices to damp the low frequency oscillation. Fourier transform of transient stability simulation results identifies the frequencies of the dominant oscillation modes accurately. Inverse transformation of the state matrix with complex shift equal to the angular speed determined by Fourier transform enhances the ability of Hessenberg method to compute the dominant modes with good selectivity and small size of Hessenberg matrix. Any specified convergence tolerance is achieved using the iterative scheme of Hessenberg method. Siting FACTS devices such as SVC, STACOM, TCSC, TCPR and UPFC has been studied using the eigen-sensitivity theory of augmented matrix. Application results of the improved Hessenberg method and eigen-sensitivity to New England 10-machine 39-bus and KEPCO systems are presented.

• 대한전기학회논문지:전력기술부문A
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• 제49권4호
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• pp.168-176
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• 2000

This paper presents the Hessenberg method, a new sparsity-based small signal stability analysis program for large interconnected power systems. The Hessenberg method as well as the Arnoldi method computes the partial eigen-solution of large systems. However, the Hessenberg method with pivoting is numerically very stable comparable to the Householder method and thus re-orthogonalization of the krylov vectors is not required. The fractional transformation with a complex shift is used to compute the modes around the shift point. If only the dominant electromechanical oscillation modes are of concern, the modes can be computed fast with the shift point determined by Fourier transforming the time simulation results for transient stability analysis, if available. The program has been successfully tested on the New England 10-machine 39-bus system and Korea Electric Power Co. (KEPCO) system in the year of 2000, which is comprised of 791-bus, 1575-branch, and 215-machines. The method is so efficient that CPU time for computing five eigenvalues of the KEPCO system is 3.4 sec by a PC with 400 MHz Pentium IIprocessor.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1123-1126
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• 1990

A new controller design algorithm based on the Hessenberg form for linear control systems has een proposed. The controller is composed of the dynamic compensator and the state feedback (dynamic state feedback). The algorithm gives a simple way to assign the eigenstructure (eigenvalues and eigenvectors) of the closed loop system and it also provides a method to assign the frequency shapes near the corner frequencies of the closed loop transfer function matrix. Because of this property, the algorithm is called the independent frequency shape control (IFSC) method.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1998년도 하계학술대회 논문집 C
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• pp.871-874
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• 1998

It is most important in small signal stability analysis of large scale power systems to compute only the dominant eigenvalues selectively with numerical stability and efficiency. Hessenberg process is numerically very stable and identifies the largest eigenvalues in magnitude. Hence, transformed system matrix must be used with the process. Inverse transformation with complex shift provides high selectivity centered on the shift, but does not possess the desired property of computing the dominant mode first. Thus, advantage of high selectivity of the transformation can be fully utilized only when the complex shift is given close to the dominant eigenvalues. In this paper, complex shift is determined by Fourier transforming the results of dynamic simulation with PTI's PSS/E transient simulation program. The convergence in Hessenberg process is accelerated using the iterative scheme. Overall, a numerically stable and very efficient small signal stability program is obtained. The stability and efficiency of the program has been validated against New England 10-machines 39-bus system and KEPCO system.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 하계학술대회 논문집 C
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• pp.1054-1056
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• 1999

It is the most important in small signal stability analysis of large scale Power systems to compute only the dominant eigenvalues selectively with numerical stability and efficiency. In this Paper evoluted linear analysis program, transformed state matrix using Inverse transformation with complex shift and then Hessenberg process and iterative scheme are used to accelerate Hessenberg process, can calculate dominant eigenvalues. In this Paper, The accuracy of this Program has been validated against 4-machines 11-bus system and New England 10-machines 39-bus system. Also applied to KEPCO system - about 791-bus 250-machines 2500-branches, got 2568 order state matrix, and calculated two dominant modes. This analysis result equaled to result of EPRI's SSSP program to use commonly, and calculating time is faster.

• 전자공학회논문지
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• 제50권11호
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• pp.28-35
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• 2013

Krylov-Schur 반복법을 활용하여 2-차원 사각 도파관에서 나타나는 고유특성을 밝혔다. 고유 행렬 방정식은 삼각형 그물 요소의 접선을 기저벡터로 사용한 FEM(유한요소법)으로 구성하였다. 우선 Arnoldi 분해법을 이용하여 이 방정식에 대한 상위 Hessenberg 행렬을 구하였다. 그리고 QR 알골리즘을 통하여 이것을 삼각형 대각 행렬인 Shur 형태로 변형하였다. 수렴 조건에 부합된 몇몇 고유 값들이 삼각형 대각 행렬의 대각 요소에 나타났다. 이들에 대응하는 고유 모드들을 역-반복법으로 구하였다. 수렴조건에 부합되는 고유 값들은 Shur 행렬의 대각선 선두 부분으로 재배열시켰다. 이들은 나머지 고유값 및 고유모드의 쌍을 구하는 반복 과정에서 변형되지 않도록 배제되었다. 이 과정이 연속하여 서너 번 반복되었는데, 그 결과 충분한 신뢰도를 갖는 주요한 몇 개의 TM 및 TE 고유 쌍들이 구하여졌다.