  With high penetrations of renewable generation and variable loads, there is
significant uncertainty associated with power flows in DC networks such that
stability and operational constraint satisfaction are of concern. Most existing
DC network optimal power flow (DN-OPF) formulations assume exact knowledge of
loading conditions and do not provide stability guarantees. In contrast, this
paper studies a DN-OPF formulation which considers both stability and
operational constraint satisfaction under uncertainty. The need to account for
a range of uncertainty realizations in this paper's robust optimization
formulation results in a challenging semi-infinite program (SIP). The proposed
solution algorithm reformulates this SIP into a computationally tractable
problem by constructing a tight convex inner approximation of the stability set
using sufficient conditions for the existence of a feasible and stable power
flow solution. Optimal generator setpoints are obtained by optimizing over the
proposed convex stability set. The validity and value of the proposed algorithm
are demonstrated through various DC networks adapted from IEEE test cases.
