Supply–Demand Dynamics Quantification and Distributionally Robust Scheduling for Renewable-Integrated Power Systems with Flexibility Constraints

The growing penetration of renewable energy sources (RES) has exacerbated operational flexibility deficiencies in modern power systems under time-varying conditions. To address the limitations of existing flexibility management approaches, which often exhibit excessive conservatism or risk exposure in managing supply–demand uncertainties, this study introduces a data-driven distributionally robust optimization (DRO) framework for power system scheduling. The methodology comprises three key phases: First, a meteorologically aware uncertainty characterization model is developed using Copula theory, explicitly capturing spatiotemporal correlations in wind and PV power outputs. System flexibility requirements are quantified through integrated scenario-interval analysis, augmented by flexibility adjustment factors (FAFs) that mathematically describe heterogeneous resource participation in multi-scale flexibility provision. These innovations facilitate the formulation of physics-informed flexibility equilibrium constraints. Second, a two-stage DRO model is established, incorporating demand-side resources such as electric vehicle fleets as flexibility providers. The optimization objective aims to minimize total operational costs, encompassing resource activation expenses and flexibility deficit penalties. To strike a balance between robustness and reduced conservatism, polyhedral ambiguity sets bounded by generalized moment constraints are employed, leveraging Wasserstein metric-based probability density regularization to diminish the probabilities of extreme scenarios. Third, the bilevel optimization structure is transformed into a solvable mixed-integer programming problem using a zero-sum game equivalence. This problem is subsequently solved using an enhanced column-and-constraint generation (C&CG) algorithm with adaptive cut generation. Finally, simulation results demonstrate that the proposed model positively impacts the flexibility margin and economy of the power system, compared to traditional uncertainty models.