CAJ | 학술논문

BR算法是一种计算非对称矩阵全特征值的数值方法。为解决矩阵阶数增加而严重恶化BR算法数值稳定的问题，本文提出一种改进的BR算法来分析电力系统小信号稳定。为提高计算精度，该算法采用正交相似变换替代高斯变换，来执行矩阵约化和特征值迭代过程中的列消元。采用严格的行消元准则，抑制特征值迭代过程中行突刺的出现，以降低带状上 Hessenberg 矩阵的带宽和提高计算速度。结合动态节点靠后排序策略和稀疏技术，实现状态矩阵的快速求解。3个IEEE系统和3个实际系统的仿真结果表明，改进BR算法的数值稳定性比原始BR算法有显著提高，并保留了特征值计算复杂度与矩阵阶数的平方渐进成正比的特点，为小信号稳定全部特征分析方法的研究，提供了新的思路。
BR산법시일충계산비대칭구진전특정치적수치방법。위해결구진계수증가이엄중악화BR산법수치은정적문제，본문제출일충개진적BR산법래분석전력계통소신호은정。위제고계산정도，해산법채용정교상사변환체대고사변환，래집행구진약화화특정치질대과정중적렬소원。채용엄격적행소원준칙，억제특정치질대과정중행돌자적출현，이강저대상상 Hessenberg 구진적대관화제고계산속도。결합동태절점고후배서책략화희소기술，실현상태구진적쾌속구해。3개IEEE계통화3개실제계통적방진결과표명，개진BR산법적수치은정성비원시BR산법유현저제고，병보류료특정치계산복잡도여구진계수적평방점진성정비적특점，위소신호은정전부특정분석방법적연구，제공료신적사로。
The BR algorithm is a numerical method for seeking all the eigenvalues of the nonsymmetric matrix. To address the problem that matrix order’s increase greatly deteriorates the numerical stability of the BR algorithm, this paper proposed an improved BR algorithm to analyze small signal stability of the power system. To improve calculation accuracy, orthogonal transformations were used to replace Gaussian transformations for column eliminations in both the matrix reduction and the eigenvalue iterations. A strict row elimination criterion was adopted to avoid the occurrences of row spikes in the eigenvalue iterations so that the bandwidth of the banded upper Hessenberg matrix can be reduced and the computing speed can be accelerated. By means of the sparsity technique as well as the dynamic-node-sorted-later scheme, fast calculation of the state matrix was achieved. Simulations on three IEEE standard systems and three actual systems indicated that the presented method has improved significantly the numerical stability compared to the original BR algorithm, and has preserved the nature of computation complexity of eigenvalues in asymptotically square proportion to the matrix order, which offers a new idea for studying the complete eigenanalysis methods applied to the small signal stability in power systems.