Coordinated control of a wind turbine array for power maximization

• Published in: 2013 American Control Conference pp. 2898 - 2904
• Main Authors: Bitar, Eilyan, Seiler, Pete
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.06.2013
• Subjects: Aerodynamics; Arrays; Couplings; Equations; Mathematical model; Optimal Control; Wind Energy; Wind turbines
• ISBN: 1479901776; 9781479901777
• ISSN: 0743-1619
• DOI: 10.1109/ACC.2013.6580274

Wind turbines are currently operated at their peak power extraction efficiency without consideration of the aerodynamic coupling between neighboring turbines. This mode of operation leads to inefficient, sub-optimal power capture at the wind farm level. By explicitly accounting for the aerodynamic wake interactions between neighboring wind turbines within a farm, we aim to characterize optimal control policies that maximize the power captured by a collection of wind turbines operating in quasi-steady wind flow conditions. In this paper, we consider two wake interaction models, termed near-field and far-field, describing wake propagation under densely and sparsely spaced turbine arrays, respectively. Under the near-field model, we derive a closed form expression for the optimal control policy maximizing power capture for a one-dimensional array of wind turbines. Moreover, we show that the optimal control policy is both static and independent of the free stream wind velocity, being thus amenable to a decentralized implementation. We also formulate and solve numerically the problem of jointly optimizing over the control policy and placement of turbines in a one dimensional 3-turbine array under the far-field model.