Distributed Real-Time Pricing Method Incorporating Load Uncertainty Based on Nonsmooth Equations for Smart Grid

The real-time pricing mechanism of smart grid based on demand response is an effective means to adjust the balance between energy supply and demand, whose implementation will impact the user's electricity consumption behaviour, the operation, and management in the future power systems. In this paper, we propose a complementarity algorithm to solve the real-time pricing of smart grid. The Karush–Kuhn–Tucker condition is considered in the social welfare maximisation model incorporating load uncertainty to transforming the model into a system of nonsmooth equations with Lagrangian multipliers, i.e., the shadow prices. The shadow price is used to determine the basic price of electricity. The system of nonsmooth equations is a complementarity problem, which enables us to study the existence and uniqueness of the equilibrium price and to design an online distributed algorithm to achieve the equilibrium between energy supply and demand. The proposed method is implemented in a simulation system composed of an energy provider and 100 users. Simulations results show that the proposed algorithm can motivate the users’ enthusiasm to participate in the demand side management and shift the peak loading. Furthermore, the proposed algorithm can improve the supply shortage. When compared with an online distributed algorithm based on the dual optimisation method, the proposed algorithm has a significantly lower running time and more accurate Lagrangian multipliers.