Robust pricing for demand response under bounded rationality in residential electricity distribution

Abstract

This paper studies residential users’ electricity consumption in response to dynamic pricing in smart grid, from the behavioral economics angle. Particularly, this research employs a novel approach, i.e., the boundedly rational user decision (BRUD) modeling framework, which assumes users will accept an electricity consumption schedule whose total utility is within an “acceptable bound” of his/her maximum utility. Subsequently, we study the optimistic and pessimistic/robust pricing models via bi-level optimization, where the utility company minimizes the total system cost while considering the best and worst case under BRUD, respectively. In order to solve the pricing models efficiently, we present two methods, i.e., the penalty method and the Lagrangian-dual method, both with the help of cutting planes. Computational results show that the proposed dynamic pricing schemes are effective in decreasing the total system cost. Furthermore, the Lagrangian-dual-based method outperforms the penalty method due to the exploitation of the special convexity structure of the problem. Finally, when compared to solutions without considering the irrationality of user behavior, solutions from the BRUD models are more efficient in reducing total system cost. Furthermore, the additional benefits gained from considering irrationality tend to grow when user’s monetary value of convenience increases.