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

Jianzhe Liu, Bai Cui, Daniel Molzahn, Chen Chen, Xiaonan Lu, Feng Qiu

Research output: Contribution to journalArticlepeer-review

5 Scopus Citations


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 set-points are obtained by optimizing over the proposed convex stability set. The validity and effectiveness of the propose algorithm is demonstrated through various DC networks adapted from IEEE test cases.
Original languageAmerican English
Pages (from-to)904-916
Number of pages13
JournalIEEE Transactions on Control of Network Systems
Issue number2
StatePublished - 2022

NREL Publication Number

  • NREL/JA-5D00-81591


  • generators
  • load modeling
  • loading
  • power system stability
  • renewable energy sources
  • uncertainty
  • voltage


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