标题： 具有多尺度不确定性的电力系统容量扩展的嵌套交叉分解算法 显示英文标题

标题： A Nested Cross Decomposition Algorithm for Power System Capacity Expansion with Multiscale Uncertainties

摘要： 现代电力系统已经见证了可再生能源、储能、电动汽车和各种需求响应资源的迅速渗透。因此，由于这些新资源带来的变化性和不确定性，电力基础设施规划面临着更多的挑战。本研究旨在开发一个分阶段和多尺度的随机混合整数规划（MM-SMIP）模型，以捕捉电力系统容量扩展问题中的粗时间尺度不确定性，如投资成本和长期需求的随机性，以及细时间尺度不确定性，如每小时可再生能源输出和电力需求的不确定性。为了应用于实际电力系统，所产生的模型将导致极其大规模的混合整数规划问题，这些问题不仅面临众所周知的维度灾难，而且在每个阶段都有大量整数变量，计算上也存在困难。为了解决与MM-SMIP模型相关的这些挑战，我们提出了一种嵌套交叉分解算法，该算法包含两层分解，即Dantzig-Wolfe分解和L形分解。在我们的数值研究中，该算法表现出有希望的计算性能，并且特别适合并行计算，这也将通过计算结果得到证明。 显示英文摘要

摘要： Modern electric power systems have witnessed rapidly increasing penetration of renewable energy, storage, electrical vehicles and various demand response resources. The electric infrastructure planning is thus facing more challenges due to the variability and uncertainties arising from the diverse new resources. This study aims to develop a multistage and multiscale stochastic mixed integer programming (MM-SMIP) model to capture both the coarse-temporal-scale uncertainties, such as investment cost and long-run demand stochasticity, and fine-temporal-scale uncertainties, such as hourly renewable energy output and electricity demand uncertainties, for the power system capacity expansion problem. To be applied to a real power system, the resulting model will lead to extremely large-scale mixed integer programming problems, which suffer not only the well-known curse of dimensionality, but also computational difficulties with a vast number of integer variables at each stage. In addressing such challenges associated with the MM-SMIP model, we propose a nested cross decomposition algorithm that consists of two layers of decomposition, that is, the Dantzig-Wolfe decomposition and L-shaped decomposition. The algorithm exhibits promising computational performance under our numerical study, and is especially amenable to parallel computing, which will also be demonstrated through the computational results.