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

TL;DR

This paper derives autocorrelation functions for a stochastic power system model, demonstrating how critical slowing down indicators like increased autocorrelation and variance signal proximity to system bifurcations.

Contribution

It provides the first derivation of autocorrelation functions for a stochastic single machine infinite bus system, linking CSD indicators to system nonlinearities near bifurcations.

Findings

Autocorrelation and variance increase near saddle-node bifurcation.

Autocorrelation functions explain the emergence of CSD signs in power systems.

Nonlinearity influences the appearance of critical slowing down indicators.

Abstract

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.