Abstract: The real-time demand response and energy schedulingis an ideal method to adjust power balance between supply and demand in the smart grid. Its implementation has a profound impact on users' behavior, and on operation and management of the power grid. It is considered that the user has multiple power storage devices with charge and discharge function. Basing on the social welfare maximization model and ensuring that the power supply of energy supplier is stable, an optimization model of real-time demand response and energy scheduling is established. The dual problem of the model is given. On the premise of satisfying strong duality, the optimal solution of the original problem can be obtained by solving the dual problem, and the real-time electricity price for users and energy supplier is determined. In dual domain, the problem can be decomposed into two types of sub-problems:the user side and the power supply side. Then a distributed real-time demand response algorithm is designed, and its convergence is proved. The optimal solution is obtained through the interaction between the power supply side and the user side. The simulation results verify the rationality of the model and the feasibility of the algorithm.

Key words: smart grid, demand response, power storage device, distributed algorithm