With the large-scale integration of distributed energy resources (DERs) into distribution networks in the form of microgrids

the transmission-distribution-microgrid coordinated economic dispatch faces significant challenges

including heightened uncertainty

increased system nonlinearity

and a substantial computational burden. This paper proposes a hierarchical distributed coordination optimization method for transmission-distribution-microgrid systems

integrating multi- period adjustable regions (MPARs) and data-driven security regions. The method employs a recursive robust convex hull fitting approach to construct the MPAR for microgrid control variables

thereby achieving temporal decoupling of state variables such as energy storage system. Then

the MPAR of the microgrid is incorporated into the distribution network optimization model. By leveraging a data-driven voltage security region

an economic dispatch optimization model for the distribution network is formulated

enabling model-free voltage regulation and optimization for distribution networks under incomplete network parameter conditions. A hierarchical distributed solution algorithm based on multi-parameter programming and spatial equivalent projection is proposed. This approach reformulates the distribution network optimization model as a feasible region of boundary variables

facilitating the efficient solution of the multi-level optimal power flow problem for transmission- distribution-microgrid systems. Finally

the effectiveness of the proposed method is validated through simulation analysis and comparison.