  Critical slowing down (CSD) is the phenomenon in which a system recovers more
slowly from small perturbations. CSD, as evidenced by increasing signal
variance and autocorrelation, has been observed in many dynamical systems
approaching a critical transition, and thus can be a useful signal of proximity
to transition. In this paper, we derive autocorrelation functions for the state
variables of a stochastic single machine infinite bus system (SMIB). The
results show that both autocorrelation and variance increase as this system
approaches a saddle-node bifurcation. The autocorrelation functions help to
explain why CSD can be used as an indicator of proximity to criticality in
power systems revealing, for example, how nonlinearity in the SMIB system
causes these signs to appear.
