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

Linsen Song () and Gaoli Sheng
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Linsen Song: School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China
Gaoli Sheng: School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China

Mathematics, 2025, vol. 13, issue 5, 1-17

Abstract: 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.

Keywords: smart grid; complementarity problems; KKT conditions; smoothing Newton algorithm; nonsingularity; classification of electricity risks; multiple prices (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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