Existing real-time pricing models represent the supply side using only a single-unit quadratic convex cost function, which falls short of addressing the complexities arising from nonsmooth variable costs and nonconvex startup costs in practical multi-unit coordinated operations. To bridge this gap, nonsmooth cost functions on the supply side were incorporated to more accurately reflect the operational characteristics of generating units, while distributed energy storage devices on the demand side were also integrated. On this basis, a social welfare maximization model that explicitly accounts for startup costs was formulated. To tackle the discontinuity of supply-side cost functions, the convex hull method was applied to transform the original model and derive convex hull prices. By duality theory, the convex hull approximation of the primal problem can be effectively solved through its dual formulation. The simulation results show that, in unit commitment problems with nonsmooth costs, the convex hull approach successfully handles the startup cost challenge within the social welfare maximization framework. Numerical examples further verify the effectiveness of the proposed pricing mechanism as well as its performance in improving total social welfare.