EndoWake: Modeling Wind by Linear Programming for Wind Farm Layout Optimization
Abstract
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.
Related
- GPU-accelerated wind farm layout search with a distilled endogenous wake model (EndoWake)
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BibTeX
@misc{fischetti2026endowake,
title = {{EndoWake: Modeling Wind by Linear Programming for Wind Farm Layout Optimization}},
author = {Martina Fischetti and Matteo Fischetti},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40157},
eprint = {2609.40157},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40157},
}
RIS
TY - UNPB
TI - EndoWake: Modeling Wind by Linear Programming for Wind Farm Layout Optimization
AU - Martina Fischetti
AU - Matteo Fischetti
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40157
UR - https://arxiv.org/abs/2609.40157
AB - 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.
ER -