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Critical slowing down (CSD) is the phenomenon in which a system recovers moreslowly from small perturbations. CSD, as evidenced by increasing signalvariance and autocorrelation, has been observed in many dynamical systemsapproaching a critical transition, and thus can be a useful signal of proximityto transition. In this paper, we derive autocorrelation functions for the statevariables of a stochastic single machine infinite bus system (SMIB). Theresults show that both autocorrelation and variance increase as this systemapproaches a saddle-node bifurcation. The autocorrelation functions help toexplain why CSD can be used as an indicator of proximity to criticality inpower systems revealing, for example, how nonlinearity in the SMIB systemcauses these signs to appear.

Calculation of the Autocorrelation Function of the Stochastic Single Machine Infinite Bus System