发表机构
University of Seville; University of Padova（塞维利亚大学; 帕多瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对风电场布局优化中的尾流效应难题，提出内生尾流模型EndoWake，将风速作为决策变量线性建模，集成于MILP并设计分支-检查方案，实验证明有效。
AI 中文摘要
风电场布局优化问题包括在给定区域内放置给定数量的涡轮机以最大化能源生产。其主要挑战之一是涡轮机之间的尾流效应，该效应会强烈影响生产，并且是一个评估和嵌入优化框架中较为繁琐的函数。在本文中，我们引入了一种新的内生尾流模型（EndoWake），其基本思想是将每个网格点的风速视为决策变量，并通过线性传播约束与其上风邻居相连。这使得将尾流方程直接纳入混合整数线性规划（MILP）模型成为可能。随后，我们开发了这样一个MILP模型，并特别引入了一类新的有效“带状”不等式，表明它们显著加强了根界。在此基础上，我们设计了一种分支-检查方案：主问题仅保留站点变量以及每个单元和场景的一个亚图变量，整数解由精确的线性时间预言机评估，最优性割是特定于问题的“上风割”。在四扇区轴向风玫瑰下的方形网格阶梯上报告了计算结果，证明了所提出改进的有效性。
英文摘要
The Wind Farm Layout Optimization problem consists of placing a given number of turbines within a given area so as to maximize energy production. One of its main challenges is the wake effect between turbines, which can strongly affect production and is a cumbersome function to evaluate and to embed in an optimization framework. In this paper we introduce a new endogenous wake model (EndoWake), based on the idea of treating the wind speed at every grid point as a decision variable, linked to its upwind neighbors through linear propagation constraints. This makes it possible to incorporate the wake equations directly into a Mixed-Integer Linear Programming (MILP) model. We then develop such a MILP model and, in particular, introduce a new class of valid "band" inequalities, showing that they substantially strengthen the root bound. Building on this, we design a branch-and-check scheme: the master problem retains only the site variables together with one hypograph variable per cell and scenario, integer solutions are evaluated by an exact linear-time oracle, and the optimality cuts are problem-specific "upwind cuts". Computational results are reported on a ladder of square grids under a four-sector axial wind rose, demonstrating the effectiveness of the proposed improvements.
Comments30 pages + 12 pages of supplementary material (appended after the references). Replication package: https://doi.org/10.5281/zenodo.22017424
