  Controlled islanding effectively mitigates cascading failures by partitioning
the power system into a set of disjoint islands. In this paper, we study the
controlled islanding problem of a power system under disturbances introduced by
a malicious adversary. We formulate the interaction between the grid operator
and adversary using a game-theoretic framework. The grid operator first
computes a controlled islanding strategy, along with the power generation for
the post-islanding system to guarantee stability. The adversary observes the
strategies of the grid operator. The adversary then identifies critical
substations of the power system to compromise and trips the transmission lines
that are connected with compromised substations. For our game formulation, we
propose a double oracle algorithm based approach that solves the best response
for each player. We show that the best responses for the grid operator and
adversary can be formulated as mixed integer linear programs. In addition, the
best response of the adversary is equivalent to a submodular maximization
problem under a cardinality constraint, which can be approximated up to a
$(1-\frac{1}{e})$ optimality bound in polynomial time. We compare the proposed
approach with a baseline where the grid operator computes an islanding strategy
by minimizing the power flow disruption without considering the possible
response from the adversary. We evaluate both approaches using IEEE 9-bus,
14-bus, 30-bus, 39-bus, 57-bus, and 118-bus power system case study data. Our
proposed approach achieves better performance than the baseline in about $44\%$
of test cases, and on average it incurs about 12.27 MW less power flow
disruption.
