The growing integration of renewable energy generation manifests as an effective strategy for reducing carbon emissions. This paper strives to efficiently approximate the set of optimal scheduling plans (OSPs) to enhance the performance of the steady-state adaptive cruise method (SACM) of power grid, improving the ability of dealing with operational uncertainties. Initially, we provide a mathematical definition of the exact box-constrained economic operating region (EBC-EOR) for the power grid and its dispatchable components. Following this, we introduce an EBC-EOR formulation algorithm and the corresponding bi-level optimization models designed to explore the economic operating boundaries. In addition, we propose an enhanced big- M method to expedite the computation of the EBC-EOR. Finally, the effectiveness of the EBC-EOR formulation, its economic attributes, correlation with the scheduling plan underpinned by model predictive control, and the significant improvement in computational efficiency (over twelvefold) are verified through case studies conducted on two test systems..