Inertia is the foundation for AC power systems frequency stability

making critical inertia requirement (CIR) assessment vital for low-inertia risk management in new-type power systems. To efficiently and accurately analyze the system inertia threshold

this article proposed a CIR assessment based on an optimization and simulation synergetic approach. First

by elaborating on the concept of feasible inertia points (FIP) and the characteristics of CIR

a decoupling-based optimization and simulation synergetic framework of CIR was constructed. The framework core integrates a FIP optimization searching model and a multi-machine frequency response simulation model

achieving transient frequency security verification through coordinated matching of inertia and frequency regulation. Then

two adaptive inertia-correction algorithms based on heuristic search and the Koopman operator are proposed respectively

enabling synergistic interaction between optimization and simulation models to achieve efficient proactive assessment of critical inertia requirements. Finally

the effectiveness and accuracy of the proposed method are verified with an actual regional power grid.