  Severe geomagnetic disturbances (GMDs) 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, (ii) the superior
performance of distributionally robust grid operations that satisfy nonlinear,
nonconvex AC power flow equations and GIC constraints, in comparison with
standard stochastic programming-based methods during the out-of-sample testing.
