QU Deqiang, LI Junxiang, SHANG Youlin, LI Yuanyuan, LUO Shichang
In smart grid, as an important way to maintain the stability of power system, real-time pricing guides users to use electricity reasonably, and then achieves the purposes of peak shaving, valley filling, energy conservation and emission reduction. On the basis of pursuing the maximization of social welfare, a real-time pricing model for commercial users is established. Since the model is a convex optimization problem, it is solved identically to the corresponding KKT system, which can be equivalently transformed into a system of nonlinear equations via nonlinear complementary functions. However, the nonlinear complementary functions are usually non-smooth, which results in a non-smooth system of equivalent nonlinear equations, and it is difficult to apply efficient solving algorithms based on the gradient information. Smooth approximation of the nonlinear complementary functions can overcome this difficulty, but the approximation error affects the accuracy of the solution. To reduce the approximation error, a new smooth approximation function for smoothing the equivalent system of equations is proposed, and the smooth Newton algorithm is used to solve the smooth equation system. Compared with the existing algorithm, the proposed algorithm has faster solution speed and higher solution accuracy, and the comparison with the fixed electricity price mechanism indicates that the proposed real-time pricing mechanism is reasonable.
