Optimization of wind plant layouts using an adjoint approach

Abstract

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 utilityscale 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.

Simulated Annealing Algorithm for Wind Farm Layout Optimization: A Benchmark Study

“…However, GA is still actively used in various fields owing to its versatility. The mathematical programming method includes mixed-integer programming [34][35][36][37] and gradient-based optimization [38][39][40][41]. Unlike heuristics methods, it has the advantage of ensuring global optimization.…”

Realistic Wind Farm Layout Optimization through Genetic Algorithms Using a Gaussian Wake Model

“…Wind Farm Layout Optimization (WFLO) has been addressed by numerous works, which implemented different optimization methods (see the review by Herbert-Acero et al [15] and references therein). Several of them have used gradient-based WFLO solvers, such as Combinatorial optimization [16], Sequential Linear (SLP) or Quadratic (SQP) Programming [6,[17][18][19] or RANS-based gradients [20]. Most contributions, however, have used gradient-free methods, most of them in the field of Soft Computing [21] (SC).…”

“…More recently Parada et al [51] applied an up-to-date GA [52] to the Mosetti et al [44] problem. However, all WFLO contributions mentioned consider at least either a gridded, limited matrix of coordinates for the turbine positions (usually 10 × 10 squared grids [16,17,[23][24][25][29][30][31]35,36,[44][45][46]48,49,51], or either a highly idealized wind climatology [4,6,[18][19][20][26][27][28][32][33][34]37,38,47]. Regarding this last point, it has been shown that the estimate of the overall wind power output in a wind farm does not become reliable until the used wind rose attains resolutions of approximately 3°and 1 m/s [53], and "using few sectors (12 as in the common practice) will lead to impressively high but unreal improvement on power" [54].…”

Adjoint-based model predictive control for optimal energy extraction in waked wind farms

“…Adjoint methods give an efficient way of obtaining the gradient of a performance index including many decision variables, regardless of the system order. Adjoint methods have been used widely in wind energy investigations for wind farm layout optimization [34] and analyses of wind farm control [15,35] using high-fidelity models of wind farms consisting of a vast number of state variables. Considering the computational efficiency of the WFSim model, we employ an adjoint method here for computing the gradient of the MPC cost function in order to make it practical and realizable for real-time control of wind farms.…”