雅可比矩阵的奇异性检测和网络孤岛的判断

DETECTION OF JACOBIAN SINGULARITY AND NETWORK ISLANDING

提出了一种以雅可比矩阵子矩阵H为检测矩阵，来检测雅可比矩阵奇异性和网络孤岛的方法。该方法在对检测矩阵三角分解的过程中，检查其列向量的线性相关性，从而判断雅可比矩阵的奇异性，仅通过一次回代即可判断出引起雅可比矩阵奇异的原因及各孤岛的节点组成。算法简单，对牛顿法和PQ分解法都适用，只需在原有的程序上稍加扩充。大量的算例证明了该方法的正确性和有效性。

In this paper. a method is proposed for the detection of Jacobian singularity and network islanding based on checking the linear dependency among the columns of the Jacobian submatrix H during its factorisation process. All required is to perform a backward substitution calculation. An examination of the coefficients allows us to detect whether the network is islanded and to determine which buses are included in the islands. The method is simple and feasible for both the Newton method and the fast decoupled method. The procedure can be easily appended to the existing load flow program. A series of numerical examples given in the paper demonstrate the validity and efficiency of the method.