Finite-covering-based hierarchical robust flexibility and uncertainty boundary estimation for aggregated distributed energy resources

• Formal definitions and identification criteria are established for power flexibility and power uncertainty at the interface. Based on the identification results, a unified two-stage robust optimization frameworks for both microgrid-level and distribution-level are formulated to enable flexibility-boundary expansion when the interface is dispatchable and uncertainty boundary compression when it is uncertainty-dominated. • The aggregation models for thermostatically controlled loads and electric vehicles are developed by explicitly incorporating device-level constraints. For electric vehicles clusters, boundary correction method on three representative boundary-trigger cases is identified, and parameter heterogeneity is represented via clustering of real-world data. • An uncertainty set transformation method based on finite covering theory is employed to better capture the short-term stochasticity of renewable generation and load fluctuations. This reduces the conservativeness of the robust optimization solution while preserving tractability. With the large-scale integration of distributed energy resources, distribution networks and microgrids may exhibit nodal power flexibility and uncertainty depending on different configurations. In this paper, we propose a hierarchical robust boundary estimation framework of the power flexibility and uncertainty within distribution networks and microgrids, aiming to support secure day-ahead scheduling and reliable flexibility utilization under renewable and demand variability. First, the definitions and corresponding criteria of power flexibility and uncertainty are proposed, and the aggregated adjustable ranges of heterogeneous distributed energy resources containing thermostatically controlled loads and electric vehicles are modelled. Then, the robust identification model for aggregated power is developed, and the flexible boundaries expansion and uncertain boundaries compression model is designed based on the robust identification results. Meanwhile, in order to reduce the conservatism of the robust optimization, the finite covering set transformation is used to characterize the short-term stochasticity of load power and photovoltaic output. Finally, the column and constraint generation algorithm is used to solve the problem, and the effectiveness of the heterogeneous distributed energy resources aggregated boundary estimation and the uncertainty set transformation method is verified by a modified IEEE 33-bus system.