Bifurcation and Manifold Based Approach for Voltage and Oscillatory Stability Assessment and Control

Abstract

This paper presents a framework based on a bifurcation and differential manifold approach that combines identification and tracing of both saddle node and Hopf bifurcation margin boundaries. The bifurcation related margin boundary could be traced along any control scenario in a multi-control parameter space combined with any given loading scenario. This is achieved by moving from one boundary point to the next without re-tracing the entire PV curve. In addition, to take into account damping, an integration-based approach to trace the critical eigenvalue near the imaginary axis is proposed. Indices are developed to identify the critical eigenvalue to be traced for further analysis. They take into account the rate of change as well as the direction of the movement. This method in combination with maximum real part calculation provides reliable information related to margins with respect to oscillatory stability and minimum damping requirements. Eigenvalue and eigenvector sensitivities (with respect to any explicit/implicit parameters) are by products of this approach. This approach can lead to cost-based fast monitoring and control for voltage and damping related margins.