Network-Cognizant Time-Coupled Aggregate Flexibility of Distribution Systems Under Uncertainties

Bai Cui, Ahmed Zamzam, Andrey Bernstein

Research output: Contribution to journalArticlepeer-review

21 Scopus Citations


Increasing integration of distributed energy resources (DERs) within distribution feeders provides unprecedented flexibility at the distribution-transmission interconnection. To exploit this flexibility and to use the capacity potential of aggregate DERs, feasible substation power injection trajectories need to be efficiently characterized. This letter provides an ellipsoidal inner approximation of the set of feasible power injection trajectories at the substation such that for any point in the set, there exists a feasible disaggregation strategy of DERs for any load uncertainty realization. The problem is formulated as one of finding the robust maximum volume ellipsoid inside the flexibility region under uncertainty. Though the problem is NP-hard even in the deterministic case, this letter derives novel approximations of the resulting adaptive robust optimization problem based on optimal second-stage policies. The proposed approach yields less conservative flexibility characterization than existing flexibility region approximation formulations. The efficacy of the proposed method is demonstrated on a realistic distribution feeder.

Original languageAmerican English
Article number9295337
Pages (from-to)1723-1728
Number of pages6
JournalIEEE Control Systems Letters
Issue number5
StatePublished - Nov 2021

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

NREL Publication Number

  • NREL/JA-5D00-78186


  • Adaptive robust optimization
  • aggregate flexibility
  • distributed energy resource
  • distribution system


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