Articles | Volume 2, issue 1
Wind Energ. Sci., 2, 115–131, 2017
Wind Energ. Sci., 2, 115–131, 2017

Research article 10 Mar 2017

Research article | 10 Mar 2017

Optimization of wind plant layouts using an adjoint approach

Ryan N. King1,2, Katherine Dykes2, Peter Graf2, and Peter E. Hamlington1 Ryan N. King et al.
  • 1University of Colorado, Boulder, Colorado, USA
  • 2National Renewable Energy Laboratory, Golden, Colorado, USA

Abstract. Using adjoint optimization and three-dimensional steady-state Reynolds-averaged Navier–Stokes (RANS) simulations, we present a new gradient-based approach for optimally siting wind turbines within utility-scale wind plants. By solving the adjoint equations of the flow model, the gradients needed for optimization are found at a cost that is independent of the number of control variables, thereby permitting optimization of large wind plants with many turbine locations. Moreover, compared to the common approach of superimposing prescribed wake deficits onto linearized flow models, the computational efficiency of the adjoint approach allows the use of higher-fidelity RANS flow models which can capture nonlinear turbulent flow physics within a wind plant. The steady-state RANS flow model is implemented in the Python finite-element package FEniCS and the derivation and solution of the discrete adjoint equations are automated within the dolfin-adjoint framework. Gradient-based optimization of wind turbine locations is demonstrated for idealized test cases that reveal new optimization heuristics such as rotational symmetry, local speedups, and nonlinear wake curvature effects. Layout optimization is also demonstrated on more complex wind rose shapes, including a full annual energy production (AEP) layout optimization over 36 inflow directions and 5 wind speed bins.

Short summary
This paper demonstrates optimization of wind turbine locations within a utility-scale wind plant using a nonlinear flow model and gradient-based optimization techniques made possible through the use of adjoints. This represents a groundbreaking improvement in model fidelity and optimization efficiency for wind energy applications. The optimized wind farms demonstrate significant improvements in annual energy production with turbine layouts that take advantage of nonlinear flow curvature effects.