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This work presents an optimization framework to aggregate the power and energy flexibilities in an interconnected power distribution systems. The aggregation framework is used to compute the day-ahead dispatch plans of multiple and interconnected distribution grids operating at different voltage levels. Specifically, the proposed framework optimizes the dispatch plan of an upstream medium voltage (MV) grid accounting for the flexibility offered by downstream low voltage (LV) grids and the knowledge of the uncertainties of the stochastic resources. The framework considers grid, i.e., operational limits on the nodal voltages, lines, and transformer capacity using a linearized grid model, and controllable resources' constraints. The dispatching problem is formulated as a stochastic-optimization scheme considering uncertainty on stochastic power generation and demands and the voltage imposed by the upstream grid. The problem is solved by a distributed optimization method relying on the Alternating Direction Method of Multipliers (ADMM) that splits the main problem into an aggregator problem (solved at the MV-grid level) and several local problems (solved at the MV-connected-controllable-resources and LV-grid levels). The use of distributed optimization enables a decentralized dispatch computation where the centralized aggregator is agnostic about the parameters/models of the participating resources and downstream grids. The framework is validated for interconnected CIGRE medium- and low-voltage networks hosting heterogeneous stochastic and controllable resources.