  In recent years, there have been increasing concerns about how geomagnetic
disturbances (GMDs) impact electrical power systems. Geomagnetically-induced
currents (GICs) can saturate transformers, induce hot spot heating and increase
reactive power losses. These effects can potentially cause catastrophic damage
to transformers and severely impact the ability of a power system to deliver
power. To address this problem, we develop a model of GIC impacts to power
systems that includes 1) GIC thermal capacity of transformers as a function of
normal Alternating Current (AC) and 2) reactive power losses as a function of
GIC. We use this model to derive an optimization problem that protects power
systems from GIC impacts through line switching, generator redispatch, and load
shedding. We employ state-of-the-art convex relaxations of AC power flow
equations to lower bound the objective. We demonstrate the approach on a
modified RTS96 system and the UIUC 150-bus system and show that line switching
is an effective means to mitigate GIC impacts. We also provide a sensitivity
analysis of optimal switching decisions with respect to GMD direction.
