Coordinated control of a wind turbine array for power maximization

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.