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 $mathbf{big}-boldsymbol{M}$