A Smoothing Newton Method for Real-Time Pricing in Smart Grids Based on User Risk Classification

Real-time pricing is an ideal pricing mechanism for regulating the balance of power supply and demand in smart grid. Considering the differences in electricity consumption risks among different types of users, a social welfare maximization model with user risk classification is proposed in this paper. Also, a smoothing Newton method is investigated for solving the proposed model. Firstly, the convexity of the model is discussed, which implies that the local optimum of the model is also the global optimum. Then, by transforming the proposed model into a smooth equation system based on the Karush–Kuhn–Tucker (KKT) conditions, we devise a smoothing Newton algorithm integrated with Powell–Wolfe line search criteria. The nonsingularity of the corresponding function’s Jacobian matrix is obtained to ensure the stability of the proposed algorithm. Finally, we give a comparison between the proposed model and the unclassified risk model and the proposed algorithm and the distributed algorithm for real-time pricing, time-of-use pricing, and fixed pricing, respectively. The numerical results demonstrate the effectiveness of the model and the algorithm.