![]() This figure shows the number of function evaluations required to optimize the multi-dimensional Rosenbrock function versus the number of variables ( Rosenbrock, 1960). Because of this poor computational scaling, many companies and researchers have been limited in the size of wind farms they can optimize, as the number of variables typically increases with the number of turbines. This figure shows only the multimodality from two dimensions, where the true design space has 200 design variables.īecause of the multimodality of the space and the often discontinuous models used in wind farm modeling, the wind industry is heavily dependent on gradient-free techniques for wind farm layout optimization ( Herbert-Acero et al., 2014).Īlthough these methods can be highly effective for small numbers of design variables, the computational expense required to converge scales poorly, approximately quadratically, with increasing numbers of variables ( Zingg et al., 2008 Rios and Sahinidis, 2013 Lyu et al., 2014 Ning and Petch, 2016 Thomas and Ning, 2018). (b) A 3-D surface, which highlights the extreme variation of the peaks and valleys. Shown is the normalized annual energy production of a 100-turbine wind farm as a function of the location of one turbine 99 turbines remain fixed, while one is moved throughout the wind farm. Our presented method facilitates the study and both gradient-free and gradient-based optimization of large wind farms, something that has traditionally been less scalable with increasing numbers of design variables.įigure 1The complexity and multimodality of wind farm layout design space. For a 100-turbine wind farm, we show that optimizing the five variables of the boundary-grid method produces wind farms that perform just as well as farms where the location of each turbine is optimized individually, which requires 200 design variables. This parameterization uses only five variables to define the layout of a wind farm with any number of turbines. To solve these issues, we present the boundary-grid parameterization. Thus, many companies and researchers have been limited in the size of wind farms they can optimize. Unfortunately, the computational expense required with these methods scales poorly with increasing numbers of variables. ![]() ![]() The wind farm layout optimization problem is notoriously difficult to solve because of the large number of design variables and extreme multimodality of the design space.īecause of the multimodality of the space and the often discontinuous models used in wind farm modeling, the wind industry is heavily dependent on gradient-free techniques for wind farm layout optimization. ![]()
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