潮流Jacobian矩阵的正规性指标

Indices for Evaluating Normality of Power Flow Jacobian Matrix

为衡量潮流Jacobian矩阵的正规程度,根据正规矩阵的定义,正规矩阵Schur分解的特点,正规矩阵的奇异值与特征值的关系,以及正规矩阵的(反)Hermite部分的奇异值与正规矩阵的特征值实部(虚部)的关系,采用F-范数,2-范数或加权和的形式,建立了衡量矩阵正规程度的指标。在IEEE 30系统上进行的仿真表明:根据矩阵的奇异值和特征值得到的加权和指标应首先考虑,由矩阵的Schur分解得出的各指标大体相同。并对潮流Jacobian矩阵的正规程度与对称程度的关系进行了探讨。

In order to quantify the normality of a matrix,according to the definition,the characteristics of the Schur factorization,and the relationship between singular values and eigenvalues of the normal matrix including the relationship between singular values of（skew-）Hermite part of normal matrix and（imaginary）real part of eigenvalues of of normal matrix,in the form of F-norm,2-norm or weight sum of a matrix,the normality indices were established.The simulations on IEEE 30 system show that,the indices derived from weight sum of singular values and eigenvalues are preferred,the indices derived from Schur factorization are approximately the same,and the relationship between normality and symmetry of power flow Jacobian matrix are discussed.