## 1 Introduction
High prediction accuracy was achieved through intra-day rolling scheduling and real-time adjustments. In Ref. [20], a hidden layer-based attack-resilient distributed cooperative control algorithm was introduced for the secondary control of islanded microgrids. In Ref. [21], to address the intermittency of renewable energy generation, the variability in load demand, and the stochasticity of market prices, an imitation learning-based real-time decision-making solution for microgrid economic dispatch is proposed. In Refs. [22; 23; 24], to address uncertainties in multi-period systems, two-stage optimization models were developed separately, optimizing resource allocation progressively across different time scales. In Ref. [25], a distributed self-triggered privacy-preserving secondary control strategy was proposed, achieving control objectives while protecting initial and real-time values. In Ref. [26], the integrated energy systems are optimally scheduled by comprehensively applying different uncertainty optimization methods at various time scales, taking into account the characteristic that the uncertainty of prediction error decreases as the prediction time scale shortens. In Ref. [27], an attention-based conditional generative adversarial network model was proposed to generate intra-day wind and PV energy scenarios. However, the aforementioned studies did not investigate the scheduling architecture of DES clusters or the internal decomposition of power commands within clusters. For the decomposition process, which involves distributing an overall control signal within the DES cluster system, a hierarchical control scheme was proposed in Ref. [28], where a novel method for calculating the constrained set of convex polytopes was introduced to reduce computational complexity. In Ref. [29], a dynamic scheduling priority assessment system for schedulable resources was developed, enabling the coordinated control of various types of schedulable resources. In Refs. [30; 31], a distributed algorithm based on alternating direction method of multipliers (ADMM) is proposed, and a parallel solving mechanism is introduced to reduce the overall computation time. In Ref. [32], a Markov chain model for populations was established and applied to the optimal control of the optimized power trajectory. However, the decomposition methods proposed in the above studies exhibit high computational complexity and impose stricter performance requirements on control terminal devices. Furthermore, the current power decomposition results do not account for the impact on the cluster's flexibility at future time steps. To address the aforementioned issues, a multi-time scale hierarchical coordinated optimization strategy for DNs with aggregated DES is proposed in this paper. The main contributions are as follows:  
1. A DES aggregation method based on the inner approximation of the Minkowski Sum is proposed, where zonotope is employed to characterize the feasible region of individual DES units, resolving the computational intractability of the Minkowski Sum in high-dimensional spaces. 2. A multi-time scale hierarchical coordinated optimization operation model for DNs based on scenario analysis and chance constraints is established, which is transformed into a second-order cone programming (SOCP) model based on the second-order cone relaxation and linearization method for quadratic constraint to improve the solution efficiency. 3. A power allocation method for the DES cluster based on the water-filling algorithm (WFA) is proposed, which preserves the total power flexibility of the DES cluster to a greater extent. The rest of the paper is organized as follows: In Section 2, the regulation requirements of DES in DNs are analyzed, and a DES aggregation model based on the inner approximation of the Minkowski Sum is established. In Section 3, a scenario generation and reduction method based on the Monte Carlo sampling method and fast non-dominated sorting technique is proposed.