Short-term voltage stability analysis in power systems: A voltage solvability indicator

Abstract

This paper presents an analytical study for short-term voltage stability based on a novel indicator. First, it is shown that the reduced Jacobian matrix of network equations can be transformed to obtain an approximately symmetric matrix which is usually positive definite when the system under study is stable. The minimum eigenvalue of the matrix is suggested as a short-term Voltage Solvability Indicator (VSI). Then, properties of the reduced conductive matrix and susceptance matrix which have significant impacts on VSI are examined. The focus of the study is power systems with multiple constant power injections, while VSI can also be applied to analyze the impact of generic power system models. It is shown that as the penetration level of constant power injections increases, VSI decreases and the system becomes more vulnerable to voltage collapse. Finally, the relationship between the eigenvalues of the reduced Jacobian matrix and the structure-preserving Jacobian matrix is established. As a result, the suggested VSI can be efficiently computed by exploring the sparsity of structure-preserving Jacobian matrix of network equations. Case studies of several test systems including a simplified 575-machine 8117-bus East China power system are reported, demonstrating the effectiveness and practicability of the proposed method.

Keywords

• Jacobian matrix
• Short-term voltage stability
• Singularity
• Positive definiteness
• Eigenvalue interlacing property