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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.