  Adaptive robust optimization (ARO) is a well-known technique to deal with the
parameter uncertainty in optimization problems. While the ARO framework can
actually be borrowed to solve some special problems without uncertain
parameters, such as the power flexibility aggregation problem studied in this
paper. To effectively harness the significant flexibility from massive
distributed energy resources (DERs), power flexibility aggregation is performed
for a distribution system to compute the feasible region of the exchanged power
at the substation over time. Based on two-stage ARO, this paper proposes a
novel method to aggregate system-level multi-period power flexibility,
considering heterogeneous DER facilities, network operational constraints, and
an unbalanced power flow model. This method is applicable to aggregate only the
active (or reactive) power, and the joint active-reactive power domain.
Accordingly, two power aggregation models with two-stage optimization are
developed: one focuses on aggregating active power and computes its optimal
feasible intervals over multiple periods, and the other solves the optimal
elliptical feasible regions for the aggregate active-reactive power. By
leveraging the ARO technique, the disaggregation feasibility of the obtained
feasible regions is guaranteed with optimality. Numerical simulations on a
real-world distribution feeder with 126 multi-phase nodes demonstrate the
effectiveness of the proposed method.
