  This paper addresses the transmission network expansion planning problem
under uncertain demand and generation capacity. A two-stage adaptive robust
optimization framework is adopted whereby the worst-case operating cost is
accounted for under a given user-defined uncertainty set. This work differs
from previously reported robust solutions in two respects. First, the typically
disregarded correlation of uncertainty sources is explicitly considered through
an ellipsoidal uncertainty set relying on their variance-covariance matrix. In
addition, we describe the analogy between the corresponding second-stage
problem and a certain class of mathematical programs arising in structural
reliability. This analogy gives rise to a relevant probabilistic interpretation
of the second stage, thereby revealing an undisclosed feature of the worst-case
setting characterizing robust optimization with ellipsoidal uncertainty sets.
More importantly, a novel nested decomposition approach based on results from
structural reliability is devised to solve the proposed robust counterpart,
which is cast as an instance of mixed-integer trilevel programming. Numerical
results from several case studies demonstrate that the effect of correlated
uncertainty can be captured by the proposed robust approach.
