Uncertainty, if not explicitly accounted for in controller design, can significantly degrade the optimal control performance of greenhouse production systems. Scenario-based stochastic MPC (SMPC) addresses uncertainty by approximating its underlying probability distributions through sampling. However, SMPC rapidly becomes computationally intractable and can suffer from growing uncertainty with longer prediction horizons. Terminal costs and constraints ensure closed-loop performance of SMPC, but designing these for greenhouse systems is challenging since they rely on steady-state targets that often do not exist in greenhouse production systems. To overcome these challenges, this work introduces RL-SMPC, which uses reinforcement learning (RL) to learn a control policy that constructs both terminal region constraints and a terminal cost function. Additionally, this policy serves as a nonlinear feedback policy to attenuate uncertainty growth in the open-loop solution of scenario-based SMPC. RL-SMPC's closed-loop performance is compared against standalone RL, MPC, and scenario-based SMPC on a greenhouse lettuce model under parametric uncertainty. Simulation results showed that RL-SMPC outperformed MPC across all prediction horizons and surpassed SMPC for horizons shorter than five hours. Moreover, the results indicated that at equal online computational cost, RL-SMPC outperformed SMPC.

Active power control for wind farms is needed to provide ancillary services. One of these services is to track a power reference signal with a wind farm by dynamically de- and uprating the turbines. Due to the stochastic nature of the wind, it is necessary to take this stochastic behavior into account when evaluating control signals. In this paper we present a closed-loop stochastic wind farm controller that evaluates thrust coefficients providing power tracking under uncertain wind speed measurements. The controller is evaluated in a high-fidelity wind farm model simulating a 9-turbine wind farm to demonstrate the stochastic controller under different uncertainty levels on the wind speed measurement and different controller settings. Results illustrate that a stochastic controller provides better tracking performance with respect to its deterministic variant.

In this paper, a model predictive control (MPC) is proposed for wind farms to minimize wake-induced power losses. A constrained optimization problem is formulated to maximize the total power production of a wind farm. The developed controller employs a two-dimensional dynamic wind farm model to predict wake interactions in advance. An adjoint approach as an efficient tool is utilized to compute the gradient of the performance index for such a large-scale system. The wind turbine axial induction factors are considered as the control inputs to influence the overall performance by taking the wake interactions into account. A layout of a 2 × 3 wind farm is considered in this study. The parameterization of the controller is discussed in detail for a practical optimal energy extraction. The performance of the adjoint-based model predictive control (AMPC) is investigated with time-varying changes in wind direction. The simulation results show the effectiveness of the proposed approach. The computational complexity of the developed AMPC is also outlined with respect to the real time control implementation.

The non-dispatchable variability of wind power production presents a substantial challenge to electric system operators who are assigned the task of balancing the demand and generation at each moment at the lowest possible cost while maintaining ultra-high system reliability. The economic factor is the key component of this problem since one can always adequately manage variability and maintain reliability if cost is not considered. There are four key components to a forecasting solution that should each be optimized in order to provide maximum value to the end user: (1) high-quality and representative measurement data for input into the forecasting procedure, (2) skillful forecasting models, (3) effective communication of the critical forecast information to automated or manual decision-makers and (4) meaningful assessment of forecast performance to provide users with confidence in using the forecast information for decision-making.

Active power control for wind farms is needed to provide ancillary services. One of these services is to track a power reference signal with a wind farm by dynamically de- and uprating the turbines. In this paper we present a closed-loop wind farm controller that evaluates 1) thrust coefficients on a seconds-scale that provide power tracking and minimize dynamical loading on a farm level and 2) yaw settings on a minutes-scale that maximize the possible power that can be harvested by the farm. The controller is evaluated in a high-fidelity wind farm model. A six-turbine simulation case study is used to demonstrate the time-efficient controller for different controller settings. The results indicate that, with a power reference signal below the maximal possible power that can be harvested by the farm with non-yawed turbines, both tracking and reduction in dynamical loading can be ensured. In a second case study we illustrate that, when a wind farm power reference signal exceeds the maximal possible power that can be harvested with non-yawed turbines for a time period, it can not be tracked sufficiently. However, when solving for and applying optimized yaw settings, tracking can be ensured for the complete simulation horizon.

As the diameters of wind turbine rotors increase, the loads across the rotors are becoming more uneven due to inhomogeneous wind fields. Therefore, more advanced passive or active load reduction techniques are introduced to mitigate these uneven loads. Furthermore, measuring the disturbance can help to improve the control performance. This paper first examines how robust stability and performance are affected by uncertain sensor measurements when an integrator-based feedback is extended with an inversion-based feedforward individual pitch controller with similar bandwidth. A fixed-structured H_∞feedback-feedforward controller is proposed. The proposed feedback-feedforward controller ensures robust stability and performance and achieves better load reduction than a classical integrator-based feedback controller combined with inversion-based feedforward controller.

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.

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.

In this paper, we present an implementation of a model predictive controller (MPC) for wind farm power tracking problem. The controller is evaluated in the high-fidelity PAral-lelized Large-eddy simulation Model (PALM). By taking measurements from PALM, we show that the closed-loop MPC can provide power reference tracking while reducing force variations on a farm level by solving a constrained optimization problem at each time step. A six turbine wind farm case study is presented in which the controller operates with yawed turbines that increases the potential power that can be harvested with the wind farm, and we show that it is possible to track a reference power signal that temporarily exceeds the power harvested when operating under the so-called greedy control settings.

The objective of active power control in wind farms is to provide ancillary grid services. Improving this is vital for a smooth wind energy penetration in the energy market. One of these services is to track a power reference signal with a wind farm by dynamically de- and uprating the turbines. In this paper we present a computationally efficient model predictive controller (MPC) for computing optimal control signals for each time step. It is applied in the PArallelized Large-eddy simulation Model (PALM), which is considered as the real wind farm in this paper. By taking measurements from the PALM, we show that the closed-loop controller can provide power reference tracking while minimizing variations in the axial forces by solving a constrained optimization problem at each time step. A six turbine simulation case study is presented in which the controller operates with optimised turbine yaw settings. We show that with these optimized yaw settings, it is possible to track a power signal that temporarily exceeds the power harvested when operating under averaged greedy control turbine settings. Additionally, variations in the turbine's force signals are studied under different controller settings.

This work presents the next step in realizing lidar-based closed-loop wake redirection control. Lidar-based closed-loop wake redirection aims at repositioning the wake at a desired position by yawing the wind turbine. The actual wake deflection is derived from lidar measurements and used in a closed-loop control scheme. Compared to an open-loop setting in which temporal changes are not taken into account, lidar-based closed-loop wake redirection can react on temporal disturbances. This yields a more robust control solution due to the employed closed-loop control framework. In this work, for the first time, the concept is implemented in an LES environment namely the PArallelized Large-eddy simulation Model (PALM) code. In PALM lidar measurements are simulated using a lidar model which are processed to estimate the wake position. A controller is synthesized by the usage of a the reduced order wind farm model WindFarmSimulator (WFSim). High-fidelity simulation results illustrate the controller's ability to adapt to a temporal changing crosswind disturbance in a turbulent simulation scenario. Consequently, it increases the power output of the two-turbine scenario compared to the open-loop approach.

Wind farm control research typically relies on computationally inexpensive, surrogate models for real-time optimization. However, due to the large time delays involved, changing atmospheric conditions and tough-to-model flow and turbine dynamics, these surrogate models need constant calibration. In this paper, a novel real-time (joint state-parameter) estimation solution for a medium-fidelity dynamical wind farm model is presented. In this work, we demonstrate the estimation of the freestream wind speed, local turbulence, and local wind field in a two-turbine wind farm using exclusively turbine power measurements. The estimator employs an Ensemble Kalman filter with a low computational cost of approximately 1.0 s per timestep on a dual-core notebook CPU. This work presents an essential building block for real-time wind farm control using computationally efficient dynamical wind farm models.

For short-term power predictions and estimations of the available power during curtailment of a wind farm, it is necessary to consider the flow dynamics and aerodynamic interactions of the turbines. In this paper, a control-oriented dynamic two-dimensional wind farm model is introduced that aims to incorporate real-time measurements such as flow velocities at turbine locations to estimate the ambient wind farm flow. The model is intended to derive flow predictions for real-time applications. Since fully resolved computational fluid dynamics are too CPU-intensive for such a task, the dynamic model presented in this paper relies on an approximation of the flow equations in a two-dimensional framework. A semi-Lagrangian advection scheme and a step-wise flow solver together offer fast calculation speed, which scales linearly with the number of grid points. In order to emulate effects of realistic three-dimensional wind farm flow, a relaxation of the two-dimensional continuity equation is presented. Furthermore, with little extra computational expense, additional dynamic state variables for various possible applications can be propagated along the wind flow. For instance, a dynamic confidence parameter can provide estimations of the accuracy of flow predictions, while a turbulence parameter adds the possibility to estimate wake induced loads on downstream turbines. In order to demonstrate the performance and validity of the new model it is compared with other models. At first a two turbine reference case is compared with a steady-state model and secondly with results obtained by the dynamic wind farm flow model WFSim. Finally a small wind farm is simulated in order to show the computational scaling of the model.

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.

Wind turbine wake redirection is a promising concept for wind farm control to increase the total power of a wind farm. Further, the concept aims to avoid partial wake overlap on a downwind wind turbine and hence aims to decrease structural loads. Controller for wake redirection need to account for model uncertainties due to the complexity of wake dynamics. Therefore, this work focuses first on modeling a wind farm using an uncertain plant description and second on the design of a robust H_∞ controller for closed-loop wake redirection by applying standard robust modeling and control techniques on a wind farm. The wake center position is estimated and fed back to a controller which uses the yaw actuator to redirect the wake. For several inflow conditions, step simulations are conducted and system identifications are performed to obtain multiple plant models. This set of models is used to derive a nominal plant and an uncertainty set. Both the nominal model and the uncertainty set define the uncertain plant model. The robust controller is then designed showing promising results in a medium-fidelity CFD simulation model with time-varying inflow conditions.