Cross-Scale Energy Constraint Propagation in Multi-Timescale Energy Storage

With increasing renewable integration and declining system inertia, battery energy storage systems (BESS) are increasingly used for fast frequency support under constrained operating conditions. However, multi-timescale BESS actions share the same state-of-charge (SOC) carrier, so short-term support may improve immediate frequency performance while reducing the terminal readiness required for sustained operation. This paper proposes a readiness-consistent assessment framework for multi-timescale BESS participation in grid-support scheduling, based on SOC propagation and synergy screening. A unified propagation model and a disturbance-response identification model are developed to characterize cross-scale support behavior, and an event-level synergy gain is paired with an SOC readiness budget to distinguish beneficial but unacceptable operating points from readiness-consistent support actions. Simulations on a structured 90-event set show clear margin dependence: as the initial SOC increases from 0.20 pu to 0.85 pu, the readiness-consistent positive-synergy probability rises from 18% to 90%, and the mean synergy gain improves from -0.018 Hz·s to 0.069 Hz·s. These results show that synergy should be evaluated jointly with terminal SOC readiness rather than in isolation.