@article{zhe-wan-sha-zha-liy-22-aa-powflow,
  author = {Zheng, Wendi and Wang, Xiangjie and Shao, Zhenguo and Zhang, Min and Li, Yixin},
  title = {A Modified Affine Arithmetic-Based Interval Optimization for Integrated Energy System with Multiple Uncertainties},
  journal = {Journal of Renewable and Sustainable Energy},
  volume = {14},
  number = {1},
  pages = {016302},
  year = 2022,
  doi = {10.1063/5.0079306},
  comment = {Modified AA?},
  abstract = {In integrated energy systems, uncertainties cause day-ahead scheduling plans to be uncertain rather than an exact solution. However, traditional interval optimization models ignore the correlation between variables, resulting in an over-conservative range of solutions. To overcome this limitation, the present paper proposes a modified affine arithmetic to establish an interval optimal scheduling model based on deterministic optimization. The correlation between different variables is tracked by sharing noise terms, and the solution in affine form is transformed into a more intuitive interval solution by a modified affine approximation method and linear relaxation method. Finally, with the minimum midpoint and radii of daily operating cost interval as the objective function, the multi-objective function is converted into a single-objective function through Lagrange multiplication to solve the model. In a case study, the proposed method is compared with the Monte Carlo simulation method and the traditional interval optimization method without affine arithmetic. The simulation results show that the radii of the interval solutions obtained by the proposed method is 9.39{\%} less than the traditional interval arithmetic at the 15{\%} level of uncertainty.}
}