中文摘要：

基于降阶潮流雅可比矩阵的V-Q灵敏度、模态分析等静态分析方法在分析电压稳定方面得到了广泛应用，但降阶雅可比矩阵涉及到系统潮流雅可比矩阵的子矩阵Pθ可逆的问题，针对此问题，该文首先结合数学矩阵理论及电力系统的实际情况就矩阵Pθ提可逆矩阵给出明确的证明，为基于降阶雅可比矩阵的应用提供理论支持。最后以新英格兰39节点系统作为算例，通过分析计算矩阵Pθ的行列式、模最小特征值及条件数来验证矩阵Pθ的可逆性，为电压稳定分析提供理论基础。

英文摘要：

The methods of V-Q sensitivity analysis and modal analysis based on reduced Jacobian matrix have been widely used for static analysis of power system voltage stability and have a long history. However, they are involved with the assumption that the sub-matrix Pθ is invertible. Toward this problem, a definite proof was given based on the matrix theory and the actual conditions of power system that the sub-matrix is invertible, and a theoretical foundation was provided for the application of the reduced Jacobian matrix. Finally, numerical study on New England 39-bus power system was given to illustrate and justify the result that the sub-matrix is invertible.