A TSO-DSO Coordination Framework via Analytical Representation and Monetization of PQV-Based Distribution System Flexibility

As the role of distribution system (DS) flexibility in transmission system operator (TSO) network management becomes increasingly vital, data privacy concerns hinder seamless interoperability. The notion of the feasible operating region (FOR), defined in the PQ domain, has emerged as a promising privacy-preserving approach. However, effectively leveraging FOR in TSO operations remains challenging due to three key factors: its accurate determination in large-scale, meshed DS networks; its tractable analytical representation; and its economic valuation. In the present paper, we propose a novel AC optimal power flow (OPF)-based method to construct a three-dimensional PQV-FOR, explicitly accounting for voltage variability and diverse flexibility-providing unit (FPU) characteristics. The construction process employs a two-stage sampling strategy that combines bounding box projection and Fibonacci direction techniques to efficiently capture the FOR. We then introduce an implicit polynomial fitting approach to analytically represent the FOR. Furthermore, we derive a quadratic cost function over the PQV domain to monetize the FOR. Thus, the proposed framework enables single-round TSO-DSO coordination: the DSO provides an analytical FOR and cost model; the TSO determines operating point at the point of common coupling (PCC) within the FOR-based AC-OPF; and the DSO computes FPU dispatch by solving its local OPF, without computationally intensive disaggregation or iterative coordination. Case studies on meshed DS with up to 533 buses, integrated into TS, demonstrates the method's efficiency compared to standard AC-OPF. On average, the proposed approach yields negligible cost deviations of at most 0.058% across test cases, while reducing computation times by up to 58.11%.