Singularity of reduced Jacobian matrices for identifying voltage and angle instability

This paper presents a methodology based on singularity of power flow Jacobian to identify the nature of instability in the power system networks. A new coupled [P-δ] Jacobian submatrix has been defined. Minimum singular value of this matrix along with the full Jacobian, [P-δ] and [Q-V] decoupled matrices as well as [Q-V] coupled matrix has been computed for different system loading conditions and utilized to distinguish between pure angle, pure voltage and combined voltage and angle instabilities. The application of the proposed method has been demonstrated on two IEEE test systems