Wind farm layouts optimized faster using advanced grid decomposition method
A Dantzig-Wolfe reformulation of the EndoWake model for optimal wind farm layouts
Computational Engineering, Finance, and Science
Summary
Placing wind turbines to capture the most energy is tricky because each turbine reduces wind for those downwind. The paper improves a method for arranging turbines on a grid by breaking the problem into small tiles and checking all possible turbine patterns in each tile. This approach helps find the best layout more quickly and with guarantees on how close to optimal it is. The authors tested their method on different grid sizes and wind conditions, showing it works better and faster than previous methods.
What this means in practice
- •For wind farm planners: Automatically generate optimal turbine positions on large grids to increase expected energy capture under various wind patterns.
- •For energy grid modelers: Incorporate tighter layout optimizations into larger energy system simulations for improved renewable energy predictions.
Authors
Martina Fischetti, Matteo Fischetti
Abstract
Wind Farm Layout Optimization places turbines to maximize the expected energy under a wind rose, each turbine lowering the wind downwind. In the EndoWake model the wind field is a variable, propagated by linear inequalities, and layouts are certified by branch-and-check. On a ladder of grids it certifies the $10\times10$ grid and leaves the larger grids open after one hour. We tighten the relaxation by a convexification computed rather than derived: every pattern of turbines inside a small tile of the grid is enumerated once with its power and enters the master as a column. The device is valid because the wind field is antitone, and exact, for the cubic power curve, with a Benders cut at integer layouts. Reduced-cost fixing and propagation between overlapping tiles shrink the master before the tree search, and the tree repeats the fixing at every improving incumbent. The incumbent comes from a tile heuristic or an LP dive. On the same computer as the branch-and-check, the $12\times12$ and $14\times14$ grids close in 48 and 395 seconds. The $16\times16$ grid is certified on five seeds from random starts, one job per seed, the heuristic on a GPU, in 1413 seconds under the uniform rose and 6484 seconds under a non-uniform one. Times are medians. A pre-specified test set of 36 unseen instances with forbidden cells confirms the advantage in the axial setting. Certified means closed at the solver's gap of $10^{-4}$: the optimum lies within it plus a residual of at most 0.00042%.