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Increasing penetration of distributed renewable energy sources (DRESs) has resulted in the emergence of distributed energy resource aggregators (DERAs). A DERA participates in the transmissionlevel market operated by a transmission system operator (TSO), and the DERA's resources are connected to a jurisdiction of the distribution system operator (DSO). Inspired by the structure of the Korean power industry, this study assumes a minimal DSO that cannot directly dispatch the resources in its system. In this study, we develop a detailed procedure for prequalification wherein the DSO checks the DERA's bids that are submitted to the TSO markets. The proposed prequalification enables the DSO to secure the reliability of its system by providing limited network information to the DERA. The DERA modifies its bid until potential overvoltage and overflow problems are resolved, even in the worst case, including uncertainties. The proposed prequalification process is verified using the IEEE 33-bus distribution network. Compared to previous studies, the results demonstrate that the proposed prequalification can deal with distribution system constraints, even though uncertainties are included. The proposed prequalification process can be applied to power industries where the DSO does not have the full dispatch authority on DRESs.