Preventing wind turbine tower natural frequency excitation with a quasi‐LPV model predictive control scheme

Abstract

With the ever increasing power rates of wind turbines, more advanced control techniques are needed to facilitate tall towers that are low in 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 incorporates 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. KEYWORDS model demodulation transformation, model predictive control, quasi-linear parameter varying, tower natural frequency skipping INTRODUCTIONThe tower makes up a substantial part of the total turbine capital costs, and therefore finding an optimum between its mass and manufacturing expenses is a critical trade-off. 1 For conventional towers, diameters are limited because of land-based transportation constraints. This aspect dictates the increase of wall thickness for the production of taller towers and consequently leads to increased weight and costs. Conventional tower designs are soft-stiff to locate the tower fundamental frequency outside the turbine variable-speed operational range and thereby eliminate the possibility of exciting a tower resonance by the rotor rotational or blade-passing frequency. However, with the ever increasing wind turbine power rates, a combination of technical solutions should enable future, low-cost, tall towers, by relaxing this frequency constraint. Soft-soft tower configurations form an opportunity for tall towers by their smaller tower diameters and reduced wall thickness. As a result, soft-soft towers are

Nonlinear optimal control of a ballast-stabilized floating wind turbine via externally stabilised Hamiltonian dynamics

“…J indicated by the solid line) are shown in Figure 3. 3 The natural frequency is in accordance with that provided in [21] for a land-based wind turbine. 4 This particular thrust coefficient has been selected arbitrarily.…”

“…The result provided in Theorem 1 entails that the invariant manifold of (15), which characterizes the exact solution of the associated nonlinear optimal control problem, can be stabilised by the addition of the virtual control input (21), yielding the controlled Hamiltonian dynamics (20). The result can be utilised to obtain a costate trajectory p which is arbitrarily close to the optimal one p .…”

“…Since it is not feasible to obtain analytic solutions of the HJB pde -not only in the context of the wind turbine model considered herein, but also in general -we exploit, following our aforementioned strategy, the result of Theorem 1 to provide an algorithm which utilises the solution of the ARE (19) and the corresponding quadratic function V = 1 2 x P x in place of the solution of the HJB pde. Namely, in the absence of the (21) with V = V q 5 Compute χ(t), p(t) solution of (20) solution of the HJB pde, we adopt a quadratic function 2 V in (21) and in the construction of the initial condition χ(0). The resulting open-loop strategy accounts for the nonlinearities in the model (as opposed to the linear quadratic approximation) through the dynamics (20) and requires (similarly to the LQ approximation) only the solution of the ARE (19).…”

On the Load Impact of Dynamic Wind Farm Wake Mixing Strategies

“…2. In the baseline case, a standard K-omega-squared torque control is implemented in the below-rated regime [36,37], while the blade pitch angles are kept constant at the optimal power coefficient C P to ensure maximal power generation. In the above-rated regime (i.e., when the wind speed exceeds 11.4 ms À1 ), the torque is kept constant while the collective pitch angles are controlled to ensure rated power production.…”

Individual pitch control by convex economic model predictive control for wind turbine side-side tower load alleviation

“…In addition, only negligible effects of the so-called aerodynamic damping is experienced, in contrast to the fore-aft motion [3]. In recent years, the most common control strategy used to mitigate prolonged side-side tower oscillation is the active damping by generator torque, such as the work done by Mulders, et al [4] and references therein. Although proven to be effective, power production can be affected as a side product of the load reduction activity, as demonstrated by Mulders, et al Alternatively, one may resort to the individual pitch control (IPC) to manipulate the blade in-plane forces' horizontal component; resulting in the side-side tower-top force counteracting the structural excitation [5].…”