Optimal Pricing Approach Based on Expected Utility Maximization with Partial Information

Real-time pricing is considered as a promising strategy to flatten the power consumption provided with perfect knowledge of consumers’ demand level. However, the gathering of full information of demand levels might be cumbersome or even impossible for the provider in practical scenarios. In this paper, instead of assuming the perfectly known demand levels, we investigate the problem where the provider has the sole knowledge of the probabilistic distribution of the demand levels. Furthermore, a penalty term caused by the prediction error of the consumption prediction is introduced due to the incomplete information. By solving the stochastic optimization problem, the optimal consumption prediction and optimal price to maximize the expected social welfare is derived analytically. Numerical results show that the degradation on the social welfare brought by the partial information can be less than 1% when the price and consumption prediction are well designed.