  Geomagnetic disturbances (GMDs), a result of space weather, pose a severe
risk to electric grids. When GMDs occur, they can cause geomagnetically-induced
currents (GICs), which saturate transformers, induce hot-spot heating, and
increase reactive power losses in the transmission grid. Furthermore,
uncertainty in the magnitude and orientation of the geo-electric field, and
insufficient historical data make the problem of mitigating the effects of
uncertain GMDs challenging. In this paper, we propose a novel distributionally
robust optimization (DRO) approach that models uncertain GMDs and mitigates the
effects of GICs on electric grids. This is achieved via a set of mitigation
actions (e.g., line switching, locating blocking devices, generator re-dispatch
and load shedding), prior to the GMD event, such that the worst-case
expectation of the system cost is minimized. To this end, we develop a
column-and-constraint generation algorithm that solves a sequence of
mixed-integer second-order conic programs to handle the underlying convex
support set of the uncertain GMDs. Also, we present a monolithic exact
reformulation of our DRO model when the underlying support set can be
approximated by a polytope with three extreme points. Numerical experiments on
'epri-21' system show the efficacy of the proposed algorithms and the exact
reformulation of our DRO model.
