Critical slowing-down as indicator of approach to the loss of stability

TL;DR

This paper demonstrates that critical slowing-down of fluctuations in power systems serves as an effective early warning indicator of approaching global instability, such as voltage collapse, by analyzing stochastic dynamics near bifurcation points.

Contribution

It introduces a method to detect critical slowing-down through eigenvalue analysis and autocorrelation functions, providing a practical tool for early stability assessment in power grids.

Findings

Critical slowing-down signals imminent system instability.

Single-mode analysis captures the dominant fluctuation behavior.

Autocorrelation functions can be used for early warning detection.

Abstract

We consider stochastic electro-mechanical dynamics of an overdamped power system in the vicinity of the saddle-node bifurcation associated with the loss of global stability such as voltage collapse or phase angle instability. Fluctuations of the system state vector are driven by random variations of loads and intermittent renewable generation. In the vicinity of collapse the power system experiences so-called phenomenon of critical slowing-down characterized by slowing and simultaneous amplification of the system state vector fluctuations. In generic case of a co-dimension 1 bifurcation corresponding to the threshold of instability it is possible to extract a single mode of the system state vector responsible for this phenomenon. We characterize stochastic fluctuations of the system state vector using the formal perturbative expansion over the lowest (real) eigenvalue of the system power flow Jacobian and verify the resulting expressions for correlation functions of the state vector by direct numerical simulations. We conclude that the onset of critical slowing-down is a good marker of approach to the threshold of global instability. It can be straightforwardly detected from the analysis of single-node autostructure and autocorrelation functions of system state variables and thus does not require full observability of the grid.