Project Description

Model reduction for wind energy optimization



bertin-logoThis use case was provided by our partner Bertin, within the R&D collaborative project Mecasif.


A wind turbine energy exploitation company needed to plan where to position its vertical wind turbines in its field in order to maximize the energy production. Simulation has proved to be useful in such cases. The particular challenge here, requiring model reduction is the size of the problem:

One option could be to model the complete field with 10 wind turbines and simulate the complete field with a traditional Computational Fluid Dynamics (CFD) simulation. But such approaches tend to be time demanding & costly  in terms of computing resources. And one complete simulation should then be launched for every possible configuration of the wind turbines on the field. 


Another way to do so, would be to have a lighter elementary model of the flow around one single wind turbine, and launching a set of Design of Experiment (DoE) with an assembly of several of such elementary model.

This is the approach that we are going to detail here, as it allow to find a good configuration at a reasonable development cost (without having the biggest computer running for hours).


The reduced model implemented in Scilab is based on the following methods:

  • Perform FEM simulation on your prefered solver, on significants configurations (boundary limits, meshing and equations of the problem)
  • Import the data of your FEM simulation in Scilab
  • Train the reduced model on this dataset
  • Validate this model on other datasets


The model reduction method performed here is a Proper Orthogonal Decomposition (POD). It consists in finding spatial “modes”, meaning a decomposition pattern reconstructing the complete model when reassembled. The image above is the complete model, and the image below is the decomposition.



On the technical side, the time of simulation of the flow around a single wind turbine was reduced, from several hours of FEM computing on a cluster, to a Scilab reduced model providing results on a regular PC station within seconds.

This technological lock being unleashed enabled running the complete model of the field composed of several reduced models on different configuration of wind turbine positions, thus finding an optimal.

This benefits of model reduction methods can be leverage in other field on similar optimization problems, running several simulation of a reduced model instead of complete costly FEM simulation.

You too, you have time-demanding and costly FEM models? We can provide you a reduced model!

Contact us for more detail.

Keywords : Model reduction, optimization, energy, Finite Element Modeling

Credits: Vertical Wind Turbine picture

The results of this study were performed and shared within the frame of the project MECASIF, funded by BPI France, and the regions Yvelines & Essone.