A cosh-based smoothing Newton algorithm for the real-time pricing problem in smart grid

Abstract

In a smart grid system, different types of electricity users such as residential, commercial and industrial users have different utility functions. This paper proposes a nonlinear constrained optimization model for real-time pricing that maximizes the total utilities of all the different user groups. A Karush–Kuhn–Tucker equation system is employed to solve the model. However, it is a challenging task to solve the system due to the nonlinear complementary condition. To tackle the challenge, a cosh-based smoothing approximation function is proposed to substitute the nonlinear complementary condition. Subsequently, the smoothing Newton algorithm is developed to solve the new equation system. The global convergence and local quadratic convergence of the algorithm are proved. Numerical experiments are performed to test the smoothing method and compare the solutions of real-time pricing, fixed pricing and time-of-use pricing strategies applied in the smart grid system. The results show that the real-time pricing mechanism is the most suitable in saving energy and reducing peaks and troughs in energy consumption. This also indicates that it is effective to use the smoothing Newton algorithm to solve the problem of real-time electricity pricing for smart grid. We obtain that the smoothing approximation function is effective for the supply–demand balance constraints in smart grid.