Characterization of power systems near their stability boundary using the sub-Gramian method

Abstract

There is increasing demand for an effective method to analyze the stability of modern power systems that are nearing their stability boundaries. This demand stems from the burgeoning use of distributed generation and renewable energy sources. We propose a new method that facilitates small-signal stability analysis of power systems, based on the spectral decomposition of a square H2 norm of the transfer function. Compared with the dynamics of the H2 and H∞ norms of the transfer functions, analyzing the behavior of individual eigen-components allows earlier identification of pre-fault conditions. Because each eigen-component is associated with a particular eigenvector, the potential sources of instability can be easily localized and tracked in real time. We analyze an important class of systems operating under pre-fault conditions near the boundary of stability. In such cases, we demonstrate that several weakly stable modes can increase the system energy up to a critical level much earlier, owing to their synergetic effect. In simulation experiments, the proposed method is applied to a stability analysis of an actual power grid on Russky Island, which is connected to an adjacent power grid on the mainland. The simulation results are analyzed and discussed. In particular, in numerical experiments we observe an interaction of weakly stable oscillating modes in the form of low-frequency beating.