  Physical consequences to power systems of false data injection cyber-attacks
are considered. Prior work has shown that the worst-case consequences of such
an attack can be determined using a bi-level optimization problem, wherein an
attack is chosen to maximize the physical power flow on a target line
subsequent to re-dispatch. This problem can be solved as a mixed-integer linear
program, but it is difficult to scale to large systems due to numerical
challenges. Three new computationally efficient algorithms to solve this
problem are presented. These algorithms provide lower and upper bounds on the
system vulnerability measured as the maximum power flow subsequent to an
attack. Using these techniques, vulnerability assessments are conducted for
IEEE 118-bus system and Polish system with 2383 buses.
