  Smart grid systems are composed of power and communication network
components. The components in either network exhibit complex dependencies on
components in its own as well as the other network to drive their
functionality. Existing, models fail to capture these complex dependencies. In
this paper, we restrict to the dependencies in the power network and propose
the Multi-scale Implicative Interdependency Relation (MIIR) model that address
the existing limitations. A formal description of the model along with its
working dynamics and a brief validation with respect to the 2011 Southwest
blackout are provided. Utilizing the MIIR model, the $K$ Contingency List
problem is proposed. For a given time instant, the problem solves for a set of
$K$ entities in a power network which when failed at that time instant would
cause the maximum number of entities to fail eventually. Owing to the problem
being NP-complete we devised a Mixed Integer Program (MIP) to obtain the
optimal solution and a polynomial time sub-optimal heuristic. The efficacy of
the heuristic with respect to the MIP is compared by using different bus system
data. In general, the heuristic is shown to provide near optimal solution at a
much faster time than the MIP.
