Analytical Representation and Monetization of Distribution System Flexibility for TSO-DSO Coordination via Advanced Sampling Techniques

As distribution system (DS) flexibility becomes crucial for transmission system operator (TSO) network management, data privacy concerns hinder effective interoperability. The notion of feasible operating region (FOR) has emerged as a promising privacy-preserving concept. 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. The present paper proposes an AC optimal power flow (OPF)-based method to construct a three-dimensional PQV-FOR that explicitly accounts 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 sampling to capture the FOR. Then, an implicit polynomial fitting approach is introduced to analytically represent the FOR. Furthermore, a quadratic cost function is derived over the PQV domain to monetize the FOR. The resulting framework enables single-round TSO-DSO communication without iterative exchanges. Case studies on meshed DS with up to 533 buses, integrated into TSs, demonstrate 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 online computation times by up to 58.11%.