Robust Flexibility Aggregation of Virtual Power Plants Considering Commercial Constraints and Temporal Decoupling

Driven by the accelerated transition toward low-carbon power systems, Virtual Power Plants (VPPs) have emerged as an essential paradigm for aggregating distributed energy resources (DERs). Consequently, accurately characterizing the aggregated multi-dimensional feasible region (FR) of VPPs is imperative to facilitate coordinated dispatch and support the secure and economic operation of the upstream grid. However, constrained by the neglect of retail price elasticity, the inability to quantify subjective user default risks, and the computational complexity of high-dimensional inter-temporal coupling, traditional purely physical modeling approaches often overestimate flexibility and suffer from the curse of dimensionality. To address these issues, a multi-dimensional robust FR characterization framework for VPPs considering commercial constraints and inter-temporal decoupling is proposed in this paper. First, a dual-coupled VPP aggregation model integrating physical boundaries and commercial retail mechanisms is formulated. Second, a robust uncertainty budget mapping mechanism based on user credit profiles is developed to comprehensively quantify the dual uncertainties of meteorological randomness and human behavioral defaults. Finally, a projection-based FR characterization method utilizing epigraph theory and Lyapunov optimization is proposed to decouple complex inter-temporal constraints with single-round VPP-ISO coordination and an iterative internal boundary-construction procedure. Simulation results on a modified 33-node active distribution network verify the effectiveness of the proposed framework.