  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 paper
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 paper
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.
