SUMMARYThis paper focuses on the problem of wind turbine fatigue load reduction by means of individual pitch control (IPC). The control approach has a two-degree-of-freedom structure, consisting of an optimal multivariable LQG controller and a feedforward disturbance rejection controller based on estimated wind speed signals. To make the control design problem time invariant, all signals are transformed to the non-rotating reference frame using the Coleman transformation. In the Coleman domain, the LQG control objective is minimization of the rotor tilt and yaw moments, whereas the feedforward controller tries to achieve even further improvement by rejecting the influence of the low-frequency components of the wind on the rotor moments. To this end, the tilt-and yaw-oriented components of the blade-effective wind speeds are approximated using stochastic random walk models, the states of which are then augmented with the turbine states and estimated using a Kalman filter. The effects of these (estimated) disturbances on the controlled outputs are then reduced using stable dynamic model inversion. The approach is tested and compared with the conventional IPC method in simulation studies with models of different complexities. The results demonstrate very good load reduction at not only low frequencies (1p blade fatigue load reduction) but also at the 3p frequency, giving rise to fatigue load reduction of the non-rotating turbine components.

The problem of designing a globally optimal full-order output-feedback controller for polytopic uncertain systems is known to be a non-convex NP-hard optimization problem, that can be represented as a bilinear matrix inequality optimization problem for most design objectives. In this paper a new approach is proposed to the design of locally optimal controllers. It is iterative by nature, and starting from any initial feasible controller it performs local optimization over a suitably defined non-convex function at each iteration. The approach features the properties of computational efficiency, guaranteed convergence to a local optimum, and applicability to a very wide range of problems. Furthermore, a fast (but conservative) LMI-based procedure for computing an initially feasible controller is also presented. The complete approach is demonstrated on a model of one joint of a real-life space robotic manipulator.

The wind turbines within a wind farm impact each other's power production and loads through their wakes. Wake control strategies, aiming to reduce wake effects, receive increasing interest by both the research community and the industry. A number of recent simulation studies with high fidelity wake models indicate that wake mitigation control is a very promising concept for increasing the power production of a wind farm and/or reducing the fatigue loading on wind turbines' components. The purpose of this paper is to study the benefits of wake mitigation control in terms of lifetime power production and fatigue loading on several existing full-scale commercial wind farms with different scale, layouts, and turbine sizes. For modeling the wake interactions, Energy Research Centre of the Netherlands' FarmFlow software is used: a 3D parabolized Navier-Stokes code, including a kturbulence model. In addition, an optimization approach is proposed that maximizes the lifetime power production, thereby incorporating the fatigue loads into the optimization criterion in terms of a lifetime extension factor. KEYWORDS active wake control, fatigue loads reduction, power production maximization, wake mitigation, wind farm control INTRODUCTIONWind turbines are being densely clustered in wind farms and effect each other's power production and loading through their wakes. Because of the reduced wind velocity and increased turbulence, a turbine operating in the wake of another turbine will produce less power and experience increased fatigue loading. Still, the common practice is to let each wind turbine maximize its individual power capture, thereby disregarding its effect on other turbines. This "greedy" approach is not optimal with respect to the power production of the whole wind farm. At the beginning of this century, researchers started the development of a cooperative approach to operate wind farms 1-3 that aim at maximizing the power production of the whole farm, while at the same time, trying to reduce the fatigue loading on the wind turbines. These methods for mitigation of wake effects are called here active wake control (AWC).There are 2 major classes of AWC methods. The first concept aims at reducing the wake deficit downstream by reducing the axial induction factor of upstream wind turbines, known as axial induction control (also referred to as heat and flux or pitch-based AWC). This is achieved by operating the turbines at the windward side at an increased blade pitch angle. 4,5 In practice, increased pitch angle could indirectly be achieved by reducing the power production of the turbine (derating). While the power production of the derated machines decreases, the wind velocity in their wakes increases, allowing to produce more power at downstream wind turbines, and, possibly, raises the overall farm production. Initial experiments in a wind tunnel 5,6 and in the field 7 have shown that the power production of a wind farm may potentially increase under pitch-based AWC. However, more-recent high-fidelity simulations 8 a...

a b s t r a c tThe aim of this paper is to develop a controller for wind farms to optimize the load and power distribution. In this regard, the farm controller calculates the power reference signals for individual wind turbine controllers such that the sum of the power references tracks the power demanded by a system operator. Moreover, the reference signals are determined to reduce the load acting on wind turbines at low frequencies. Therefore, a trade-off is made for load and power control, which is formulated as an optimization problem. Afterwards, the optimization problem for the wind farm modeled as a bilinear control system is solved using an approximation method.

If you want to cite this report, please use the following reference instead:S. Kanev, B. De Schutter, and M. Verhaegen, "The ellipsoid algorithm for probabilistic robust controller design," Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, pp. 2248-2253, Dec. 2002 This paper presents a new iterative approach to probabilistic robust controller design, which is an alternative to the recently proposed Subgradient Iteration Algorithm (SIA). In its original version [12] the SIA possesses the useful property of guaranteed convergence in a finite number of iterations, but requires that the radius of a non-empty ball contained in the solution set is known a-priori. This rather restrictive assumption was later on released in [3], but only at the expense of an increased number of iterations. The approach in this paper does also not require the knowledge of such a radius, and offers a significant improvement even over the original SIA in terms of the maximum number of possible correction steps that can be executed before a feasible solution is reached. Given an initial ellipsoid that contains the solution set, the approach iteratively generates a sequence of ellipsoids with decreasing volumes, all containing the solution set. A method for finding an initial ellipsoid containing the solution set is also proposed. The approach is illustrated on a real-life diesel actuator benchmark model.

This paper focuses on the problem of extreme wind gust and direction change recognition (EG&DR) and control (EEC). An extreme wind gust with direction change can lead to large loads on the turbine (causing fatigue) and unnecessary turbine shutdowns by the supervisory system caused by rotor overspeed. The proposed EG&DR algorithm is based on a non-linear observer (extended Kalman fi lter) that estimates the oblique wind infl ow angle and the blade effective wind speed signals, which are then used by a detection algorithm (cumulative sum test) to recognize extreme events. The nonlinear observer requires that blade root bending moments measurements (in-plane and out-of-plane) are available. Once an extreme event is detected, an EEC algorithm is activated that: (i) tries to prevent the rotor speed from exceeding the overspeed limit by fast collective blade pitching; and (ii) reduces 1p blade loads by means of individual pitch control algorithm, designed in an H ∞ optimal control setting. The method is demonstrated on a complex non-linear test turbine model.

Wake redirection is a wind farm control strategy that aims at increasing the overall power yield of a wind farm. It involves intentional misalignment of the rotors of upstream wind turbines with respect to the wind direction, thereby diverting their wakes aside from downstream turbines. The yaw misalignment angles are typically optimized using static wake models. In real-life, due to the rapid fluctuations of the wind direction with time, the optimized yaw misalignment angles cannot be instantaneously tracked as this would inevitably require an unacceptable amount of rotor yawing. This work is focused on how to dynamically adapt the statically optimzied yaw misalignment angles to achieve a good balance between high energy gain and limited yaw actuator duty cycle.

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