  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 the location of increased stress, while growth of
autocorrelation in certain line currents is a reliable indicator of system-wide
instability.
