Region-based flexibility quantification in distribution systems: An analytical approach considering spatio-temporal coupling

Operational flexibility is to depict the ability of a power system in guaranteeing a secure and high-performance system operation, which is essential for distribution systems (DSs) with high renewable energy generation (REG) penetration. However, due to the dispersed integration of energy storage systems and uncertain REGs, the available regulation capability exhibits spatio-temporal coupling. It poses a challenge to quantify flexibility considering multiple locations and time periods. This paper proposes a novel analytical region-based method to characterize the flexibility considering spatio-temporal coupling, where the total dispatch budget and carbon emission constraints are considered to guarantee economic and environmental benefits. Leveraging the basic feasible solution theory, we derive an analytical formulation of the flexibility region, expressed as a set of linear inequalities. Note that no inner or outer approximation techniques are employed in the deduction procedure. The effectiveness and scalability of the proposed method are validated on test systems. Case studies demonstrate that the proposed method enables precise quantification and visualization of operational flexibility for DSs. The derived flexibility region is a closed polyhedron in a high-dimensional space, signifying the maximum ranges of uncertainties that can be accommodated.