<p>Real-time pricing serves as an effective demand-side management tool, enabling peak shaving, load valley filling, and mitigation of energy waste. Currently, constructing a social welfare maximization model to determine real-time prices is the mainstream approach. In the social welfare maximization model, the utility function describing user satisfaction with power usage is essential. If the user utility is not accurately quantified, the real-time pricing may deviate from the actual situation. In practice, users typically have a base consumption range and an adjustable consumption range, and the impact of power usage changes on user satisfaction differs across these ranges. In order to capture the utility preferences of users in different consumption ranges precisely, this paper proposed a piecewise utility function. Since the piecewise utility function is not smooth overall, we introduced a smoothing method to globally approximate the piecewise function. Furthermore, a social welfare maximization model is constructed based on this utility function to obtain a fair power price between supply and demand. According to the separability of the variables of model, we design a dual subgradient algorithm to solve the model. Simulation results indicated the effectiveness of the proposed algorithm.</p>