In this paper, an adjoint-based model predictive control (AMPC) is proposed in order to provide active power control (APC) services of wind farms, even in the presence of problematic wake interactions. The control objective is defined to minimize wind farm power reference tracking error. The non-unique optimal distribution of wind turbine power references is a resulting by-product which can be very informative for other wind farm control methods. The developed predictive controller employs a medium-fidelity 2D dynamic wind farm model to predict wake interactions at hub-height of wind turbines in advance. An adjoint approach as a computationally efficient tool is utilized to compute the gradient for such a large-scale system. The axial induction factor of each wind turbine is considered here as a control variable to influence the overall performance of a wind farm by taking the wake interactions of the wind turbines into account. The performance of the AMPC-based APC is examined for a layout of a 2×3 wind farm in a wake condition through simulation studies. The results show the effectiveness of the proposed approach and introduce some potential studies to improve and extend its performance.

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Wind turbines are often sited together in wind farms as it is economically advantageous. Controlling the flow within wind farms to reduce the fatigue loads, maximize energy production and provide ancillary services is a challenging control problem due to the underlying time-varying non-linear wake dynamics. In this paper, we present a control-oriented dynamical wind farm model called the WindFarmSimulator (WFSim) that can be used in closed-loop wind farm control algorithms. The three-dimensional Navier–Stokes equations were the starting point for deriving the control-oriented dynamic wind farm model. Then, in order to reduce computational complexity, terms involving the vertical dimension were either neglected or estimated in order to partially compensate for neglecting the vertical dimension. Sparsity of and structure in the system matrices make this model relatively computationally inexpensive. We showed that by taking the vertical dimension partially into account, the estimation of flow data generated with a high-fidelity wind farm model is improved relative to when the vertical dimension is completely neglected in WFSim. Moreover, we showed that, for the study cases considered in this work, WFSim is potentially fast enough to be used in an online closed-loop control framework including model parameter updates. Finally we showed that the proposed wind farm model is able to estimate flow and power signals generated by two different 3-D high-fidelity wind farm models.

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In this paper, we extend our closed-loop optimal control framework for wind farms to minimize wake-induced power losses. We develop an adjoint-based model predictive controller which employs a medium-fidelity 2D dynamic wind farm model. The wind turbine axial induction factors are considered here as the control inputs to influence the overall performance by taking wake interactions of the wind turbines into account. A constrained optimization problem is formulated to maximize the total power production of a given wind farm. An adjoint approach as an efficient tool is utilized to compute the gradient for such a large-scale system. The computed gradient is then modified to deal with the defined final set and practical constraints on the wind turbine control inputs. The performance of the wind farm controller is examined for a more realistic test case, a layout of a 2 x 3 wind farm with dynamical changes in wind direction. The effectiveness of the proposed approach is studied through simulations.

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This paper proposes an adjoint-based model predictive control for optimal energy extraction of wind farms. It employs the axial induction factor of wind turbines to influence their aerodynamic interactions through the wake. The performance index is defined here as the total power production of the wind farm over a finite prediction horizon. A medium-fidelity wind farm model is utilized to predict the inflow propagation in advance. The adjoint method is employed to solve the formulated optimization problem in a cost effective way and the first part of the optimal solution is implemented over the control horizon. This procedure is repeated at the next controller sample time providing the feedback into the optimization. The effectiveness and some key features of the proposed approach are studied for a two turbine test case through simulations.@en

In this paper, we present and extend the dynamic medium fidelity control-oriented Wind Farm Simulator (WFSim) model. WFSim resolves flow fields in wind farms in a horizontal, two dimensional plane. It is based on the spatially and temporally discretised two dimensional Navier-Stokes equations and the continuity equation and solves for a predefined grid and wind farm topology. The force on the flow field generated by turbines is modelled using actuator disk theory. Sparsity in system matrices is exploited in WFSim, which enables a relatively fast flow field computation. The extensions to WFSim we present in this paper are the inclusion of a wake redirection model, a turbulence model and a linearisation of the nonlinear WFSim model equations. The first is important because it allows us to carry out wake redirection control and simulate situations with an inflow that is misaligned with the rotor plane. The wake redirection model is validated against a theoretical wake centreline known from literature. The second extension makes WFSim more realistic because it accounts for wake recovery. The amount of recovery is validated using a high fidelity simulation model Simulator fOr Wind Farm Applications (SOWFA) for a two turbine test case. Finally, a linearisation is important since it allows the application of more standard analysis, observer and control techniques.

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Controlling the flow within wind farms, to increase the overall energy capture and to reduce the fatigue loads, is a challenging control problem due to its size and the underlying time-varying dynamics. State-of-the-art wind farm controllers follow the open-loop control paradigm by computing optimal set-points using static models. However, due to the time-varying inflow conditions and uncertain flow dynamics the closed-loop control paradigm should be used. In this work, a control-oriented quasi Linear Parameter Varying (LPV) descriptor model will be derived using the two dimensional (2D) Navier-Stokes equations. Sparsity of the system matrices make it possible to use this model for closed-loop controller synthesis. Some key features of the approach will be presented using a two turbine test case.

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This paper studies the active rotor load controller design for a large wind turbine via individual pitch control (IPC). A multivariable IPC is designed to reject the periodic load disturbances, in an optimal manner, by penalizing the control effort according to the pitch actuator constraints. Frequency response analysis of the well-known multi-blade coordinate (MBC) transformation describes how the rotational speed variations influence the flexible modes of the blades. Therefore, a multivariable plant is constructed in the frequency-domain, compatible with applying the disturbance rejection control approaches. Then, a mixed sensitivity H∞ optimization problem is formulated based on the obtained MIMO model. The performance of the synthesized controller is analyzed and compared with the PI-based IPC. Finally, the dynamic load mitigation of the developed controller is studied through the fatigue load analysis with a high-fidelity aeroelastic simulator. Results show a significant amount of load alleviation in return for an even lower level of the pitch activity, with respect to the PI-based IPC.@en