@article{Song2025, 
author = {Linsen Song and Yichen Du},
title = {A real-time pricing dynamic algorithm for a smart grid with multi-pricing and multiple energy generation},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {5},
pages = {2989-3006},
keywords = {smart grid, real-time pricing, multi-source power supply, multi-energy generation, distributed algorithm, pollution},
url = {https://www.sciopen.com/article/10.3934/era.2025131},
doi = {10.3934/era.2025131},
abstract = {With the proposal of the new power system, power supply from renewable energy sources and traditional power supply have emerged as the future development directions of the power grid, while the traditional pricing mechanisms are facing new challenges. Considering the different characteristics of renewable energy power supply and traditional power supply, such as being clean and sustainable, but unstable, for renewable energy power supply, and being stable and technologically mature, but causing significant pollution, for traditional power supply, a multi-price model with the cost of pollution treatment under the multi-energy electricity generation was established in this paper. A distributed algorithm with the non-dominated sorting genetic algorithm (NSGA-Ⅱ) was also proposed. In the model, the power supply side includes traditional energy generation, renewable energy generation, and the energy storage device. The proposed algorithm was designed using Lagrangian duality theory, and the multi-price is obtained by solving the different lagrange multipliers. Finally, the numerical results show that the model is reasonable when comparing the obtained price and social welfare with that untreated-pollution model, as well as a single supply model. Also, the proposed algorithm always has better computational efficiency, when compared with PSO, HS, and GA algorithms. The proposed model and algorithm provide a new idea and method for the optimal scheduling of a smart grid.}
}