电力系统小信号稳定全特征值分析的改进BR算法  

Complete Eigenanalysis of Power System Small Signal Stability Using the Improved BR Algorithm

作　　者：赵文恺[1] 严正[1] 房鑫炎[1] 王毅[2] 

机构地区：[1]电力传输与功率变换控制教育部重点实验室(上海交通大学),上海市闵行区200240 [2]中国电力科学研究院,北京市海淀区100192

出　　处：《中国电机工程学报》2014年第10期1599-1608,共10页Proceedings of the CSEE

基　　金：国家电网公司大电网重大专项资助项目(SGCC-MPLG018-2012);高等学校博士学科点专项科研基金(博导类)资助项目(20120073110020)~~

摘　　要：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。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.

关 键 词：小信号稳定 全特征值分析 BR算法 正交变换 高斯变换 

分 类 号：TM744[电气工程—电力系统及自动化]