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

Optimal Power Flow for DC Networks with Robust Feasibility and Stability Guarantees