  Severe geomagnetic disturbances increase the magnitude of the electric field
on the Earth's surface (E-field) and drive geomagnetically-induced currents
(GICs) along the transmission lines in electric grids. These additional
currents can pose severe risks, such as current distortions, transformer
saturation and increased reactive power losses, each of which can lead to
system unreliability. Several mitigation actions (e.g., changing grid topology)
exist that can reduce the harmful GIC effects on the grids. Making such
decisions can be challenging, however, because the magnitude and direction of
the E-field are uncertain and non-stationary. In this paper, we model uncertain
E-fields using the distributionally robust optimization (DRO) approach that
determines optimal transmission grid operations such that the worst-case
expectation of the system cost is minimized. We also capture the effect of GICs
on the nonlinear AC power flow equations. For solution approaches, we develop
an accelerated column-and-constraint generation (CCG) algorithm by exploiting a
special structure of the support set of uncertain parameters representing the
E-field. Extensive numerical experiments based on "epri-21" and "uiuc-150"
systems, designed for GMD studies, demonstrate (i) the computational
performance of the accelerated CCG algorithm, and (ii) the performance of
distributionally robust grid operations that satisfy nonlinear, nonconvex AC
power flow equations and GIC constraints.
