Jan-Willem van Wingerden

Bart M Doekemeijer, Paul A Fleming, Jan-Willem van Wingerden

In wind farms, wake interaction leads to losses in power capture and accelerated structural degradation when compared to freestanding turbines. One method to reduce wake losses is by misaligning the rotor with the incoming flow using its yaw actuator, thereby laterally deflecting the wake away from downstream turbines. However, this demands an accurate and computationally tractable model of the wind farm dynamics. This problem calls for a closed-loop solution. This tutorial paper fills the scientific gap by demonstrating the full closed-loop controller synthesis cycle using a steady-state surrogate model. Furthermore, a novel, computationally efficient and modular communication interface is presented that enables researchers to straight-forwardly test their control algorithms in large-eddy simulations. High-fidelity simulations of a 9-turbine farm show a power production increase of up to 11% using the proposed closed-loop controller compared to traditional, greedy wind farm operation.

Sebastiaan Paul Mulders, Atindriyo Kusumo Pamososuryo, Gianmarco Emilio Disario et al.

With the trend of increasing wind turbine rotor diameters, the mitigation of blade fatigue loadings is of special interest to extend the turbine lifetime. Fatigue load reductions can be partly accomplished using Individual Pitch Control (IPC) facilitated by the so-called Multi-Blade Coordinate (MBC) transformation. This operation transforms and decouples the blade load signals in a yaw- and tilt-axis. However, in practical scenarios, the resulting transformed system still shows coupling between the axes, posing a need for more advanced Multiple-Input Multiple-Output (MIMO) control architectures. This paper presents a novel analysis and design framework for decoupling of the non-rotating axes by the inclusion of an azimuth offset in the reverse MBC transformation, enabling the application of simple Single-Input Single-Output (SISO) controllers. A thorough analysis is given by including the azimuth offset in a frequency-domain representation. The result is evaluated on simplified blade models, as well as linearizations obtained from the NREL~5\nobreakdash-MW reference wind turbine. A sensitivity and decoupling assessment justify the application of decentralized SISO control loops for IPC. Furthermore, closed-loop high-fidelity simulations show beneficial effects on pitch actuation and blade fatigue load reductions.

Sebastiaan Paul Mulders, Tobias Gybel Hovgaard, Jacob Deleuran Grunnet et al.

With the ever increasing power rates of wind turbines, more advanced control techniques are needed to facilitate tall towers that are low-weight and cost effective, but in effect more flexible. Such soft-soft tower configurations generally have their fundamental side-side frequency in the below-rated operational domain. Because the turbine rotor practically has or develops a mass imbalance over time, a periodic and rotor-speed dependent side-side excitation is present during below-rated operation. Persistent operation at the coinciding tower and rotational frequency degrades the expected structural life span. To reduce this effect, earlier work has shown the effectiveness of active tower damping control strategies using collective pitch control. A more passive approach is frequency skipping by inclusion of speed exclusion zones, which avoids prolonged operation near the critical frequency. However, neither of the methods incorporate a convenient way of performing a trade-off between energy maximization and fatigue load minimization. Therefore, this paper introduces a quasi-linear parameter varying model predictive control (qLPV-MPC) scheme, exploiting the beneficial (convex) properties of a qLPV system description. The qLPV model is obtained by a demodulation transformation, and is subsequently augmented with a simple wind turbine model. Results show the effectiveness of the algorithm in synthetic and realistic simulations using the NREL 5-MW reference wind turbine in high-fidelity simulation code. Prolonged rotor speed operation at the tower side-side natural frequency is prevented, whereas when the trade-off is in favor of energy production, the algorithm decides to rapidly pass over the natural frequency to attain higher rotor speeds and power productions.

Karst Brummelhuis, Niranjan Saikumar, Jan-Willem van Wingerden et al.

This paper presents a novel adaptive feedforward controller design for reset control systems. The combination of feedforward and reset feedback control promises high performance as the feedforward guarantees reference tracking, while the non-linear feedback element rejects disturbances. To overcome inevitable model mismatches, the feedforward controller adapts to increase precision in reference tracking. Where linear existing adaptive feedforward controllers do not guarantee convergence in the presence of reset, this work presents a novel adaptive law based on converging and diverging regions of adaptation to achieve good tracking. Experimental results demonstrate the claimed advantage of the novel method.

Leif Erik Andersson, Bart Doekemeijer, Daan van der Hoek et al.

This article investigates the optimization of yaw control inputs of a nine-turbine wind farm. The wind farm is simulated using the high-fidelity simulator SOWFA. The optimization is performed with a modifier adaptation scheme based on Gaussian processes. Modifier adaptation corrects for the mismatch between plant and model and helps to converge to the actual plan optimum. In the case study the modifier adaptation approach is compared with the Bayesian optimization approach. Moreover, the use of two different covariance functions in the Gaussian process regression is discussed. Practical recommendations concerning the data preparation and application of the approach are given. It is shown that both the modifier adaptation and the Bayesian optimization approach can improve the power production with overall smaller yaw misalignments in comparison to the Gaussian wake model.

Joeri Frederik, Lars Kröger, Gert Gülker et al.

A commonly applied method to reduce the cost of wind energy, is alleviating the periodic loads on turbine blades using Individual Pitch Control (IPC). In this paper, a data-driven IPC methodology called Subspace Predictive Repetitive Control (SPRC) is employed. The effectiveness of SPRC will be demonstrated on a scaled 2-bladed wind turbine. An open-jet wind tunnel with an innovative active grid is employed to generate reproducible turbulent wind conditions. A significant load reduction with limited actuator duty is achieved even under these high turbulent conditions. Furthermore, it will be demonstrated that SPRC is able to adapt to changing operating conditions.

Hildo Bijl, Thomas B. Schön, Jan-Willem van Wingerden et al.

Bayesian optimization through Gaussian process regression is an effective method of optimizing an unknown function for which every measurement is expensive. It approximates the objective function and then recommends a new measurement point to try out. This recommendation is usually selected by optimizing a given acquisition function. After a sufficient number of measurements, a recommendation about the maximum is made. However, a key realization is that the maximum of a Gaussian process is not a deterministic point, but a random variable with a distribution of its own. This distribution cannot be calculated analytically. Our main contribution is an algorithm, inspired by sequential Monte Carlo samplers, that approximates this maximum distribution. Subsequently, by taking samples from this distribution, we enable Thompson sampling to be applied to (armed-bandit) optimization problems with a continuous input space. All this is done without requiring the optimization of a nonlinear acquisition function. Experiments have shown that the resulting optimization method has a competitive performance at keeping the cumulative regret limited.

Hildo Bijl, Thomas B. Schön, Jan-Willem van Wingerden et al.

There has been a growing interest in using non-parametric regression methods like Gaussian Process (GP) regression for system identification. GP regression does traditionally have three important downsides: (1) it is computationally intensive, (2) it cannot efficiently implement newly obtained measurements online, and (3) it cannot deal with stochastic (noisy) input points. In this paper we present an algorithm tackling all these three issues simultaneously. The resulting Sparse Online Noisy Input GP (SONIG) regression algorithm can incorporate new noisy measurements in constant runtime. A comparison has shown that it is more accurate than similar existing regression algorithms. When applied to non-linear black-box system modeling, its performance is competitive with existing non-linear ARX models.