The increasing integration of renewable energy sources (RESs) presents significant challenges for the safe and economical operation of power grids. Addressing the critical need to assess the effect of RES uncertainties on optimal scheduling schemes (OSSs), this paper introduces a convex hull based economic operating region (CH-EOR) for power grids. The CH-EOR is mathematically defined to delineate the impact of RES uncertainties on power grid operations. We propose a novel approach for generating the CH-EOR, enhanced by a big-M preprocessing method to improve the computational efficiency. Performed on four test systems, the proposed big-M preprocessing method demonstrates notable advancements: a reduction in average operating costs by over 10% compared with the box-constrained operating region (BC-OR) derived from robust optimization. Furthermore, the CH-EOR occupies less than 11.79% of the generators ’ adjustable region (GAR). Most significantly, after applying the proposed big-M preprocessing method, the computational efficiency is improved over 17 times compared with the traditional big-M method.