A two-stage bi-level robust optimization framework for inter-provincial ramping resource sharing under interval number uncertainty

A two-stage, two-layer robust optimization method is proposed for inter-provincial ramp resource sharing, simultaneously accounting for ramp uncertainty and dynamic interconnection capacity constraints. First, a data-driven approach generates ramp intervals to capture the correlation between day-ahead forecasts and actual intra-day ramping. Based on this, a dual uncertainty set encompassing both response fluctuations and ramp interval counts is constructed. A risk preference parameter is introduced to transform the interval counts. Finally, a two-layer robust optimization structure is formed: the upper layer handles inter-provincial coordination, while the lower layer manages intra-provincial dispatch. This structure accounts for uncertainty relationships across both the day-ahead and intra-day phases while embedding dynamic interconnection capacity constraints. To preserve the distributed nature of the problem, the Alternating Direction Method of Multipliers is employed for the solution. Case studies based on actual Chinese scenarios demonstrate that compared to independent provincial dispatch models, this approach reduces total system costs by 30.2%. Compared to traditional deterministic ramp-sharing schemes, ramping gap events are reduced by 80%.