The increasing electricity demand imposes higher requirements on the power system to generate electricity and balance the supply and demand. The unit commitment problem is critical in power systems for determining the generation schedules and market prices. However, its inherent nonconvexity and discontinuity pose significant challenges to efficient pricing. The convex hull method addresses this nonconvexity by taking the slope of the convex envelope of cost function for generating units over the convex hull of the feasible set as the price. Nevertheless, due to the nonsmoothness, the convex hull price cannot be computed by using the gradient-based methods, which increases the computational complexity. Smoothing techniques provide an effective way by converting the nonsmooth problem into a smooth one, which enhances the computational efficiency. This paper proposes a real-time pricing scheme for the smart grid that incorporates renewable energy generation and energy storage devices on the demand side and multiple generating units on the supply side. Considering the dynamic demand of users and startup costs of generating units, a social welfare maximization model is formulated. By employing the convex hull method, the convex envelopes of the cost functions for generating units are derived. The smoothing technique is then employed to convert the original model into a smooth one. Furthermore, a distributed iterative algorithm on the basis of gradient projection method is developed by leveraging the separable structure of the variables to solve the model efficiently. Simulation results validate the feasibility and effectiveness of the convex hull method for real-time pricing in smart grid with multiple generating units via smoothing technique.