Linear Analysis of Multiple Outage Interaction

Linear sensitivities are popular methods for approximating the change in power system quantities after a change in the system. This paper examines the formulas that are used to calculate line outage distribution factors (LODFs) for both single and double outages. An examination of these formulas shows cases where they break down. In particular, the formulas fail when system islanding occurs. This happens for both single and multiple line outage sensitivities. Comments are made about the use of linear sensitivities in these cases, and a metric of interaction - a measure of how close the system is brought to islanding by a particular outage is developed. This metric is proposed as a useful method of categorizing line outages. Statistics are presented for the IEEE 300-bus case showing that the distribution of the metric indicates that most double outages are nearly decoupled.