  In this paper the interactions between component failures are quantified and
the interaction matrix and interaction network are obtained. The quantified
interactions can capture the general propagation patterns of the cascades from
utilities or simulation, thus helping to better understand how cascading
failures propagate and to identify key links and key components that are
crucial for cascading failure propagation. By utilizing these interactions a
high-level probabilistic model called interaction model is proposed to study
the influence of interactions on cascading failure risk and to support online
decision-making. It is much more time efficient to first quantify the
interactions between component failures with fewer original cascades from a
more detailed cascading failure model and then perform the interaction model
simulation than it is to directly simulate a large number of cascades with a
more detailed model. Interaction-based mitigation measures are suggested to
mitigate cascading failure risk by weakening key links, which can be achieved
in real systems by wide area protection such as blocking of some specific
protective relays. The proposed interaction quantifying method and interaction
model are validated with line outage data generated by the AC OPA cascading
simulations on the IEEE 118-bus system.
