  Modern society critically depends on the services electric power provides.
Power systems rely on a network of power lines and transformers to deliver
power from sources of power (generators) to the consumers (loads). However,
when power lines fail (for example, through lightning or natural disasters) or
when the system is heavily used, the network is often unable to fulfill all of
the demand for power. While systems are vulnerable to these failures,
increasingly, sophisticated control devices are being deployed to improve the
efficiency of power systems. Such devices can also be used to improve the
resiliency of power systems to failures. In this paper, we focus on using FACTS
devices in this context. A FACTS device allows power grid operators to adjust
the impedance parameters of power lines, thereby redistributing flow in the
network and potentially increasing the amount of power that is supplied. Here
we develop new approaches for determining the optimal parameter settings for
FACTS devices in order to supply the maximal amount of power when networks are
stressed, e.g. power line failures and heavy utilization.
