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

With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and constraint satisfaction are important concerns. Most existing DC network optimal power flow (DN-OPF) formulations assume exact knowledge about loading conditions and do not provide stability guarantees. In contrast, this paper studies a DN-OPF formulation which considers both stability and 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 amenable problem whose solution provides a feasible operating point for the SIP. This algorithm constructs a convex stability set using sufficient conditions for the existence of a feasible and stable power flow solution. Solving an optimization problem based on this convex stability set provides generator set points which ensure that the DC network has a stable operating point for any considered uncertainty realization. This optimization problem takes a form similar to a deterministic DN-OPF problem and is therefore tractable. The proposed algorithm is demonstrated using various DC networks adapted from IEEE test cases.