Identifying Useful Statistical Indicators of Proximity to Instability in Stochastic Power Systems

Prior research has shown that autocorrelation and variance in voltage measurements tend to increase as power systems approach instability. This paper seeks to identify the conditions under which these statistical indicators provide reliable early warning of instability in power systems. First, the paper derives and validates a semi-analytical method for quickly calculating the expected variance and autocorrelation of all voltages and currents in an arbitrary power system model. Building on this approach, the paper describes the conditions under which filtering can be used to detect these signs in the presence of measurement noise. Finally, several experiments show which types of measurements are good indicators of proximity to instability for particular types of state changes. For example, increased variance in voltages can reliably indicate both proximity to a bifurcation and the location of increased stress. On the other hand, growth of autocorrelation in certain line currents is related less to a specific location of stress but, rather, is a reliable indicator of stress occurring somewhere in the system; in particular, it would be a clear indicator of approaching instability when many nodes in an area are under stress.