Strong stabilization of a wind turbine tower model in the plane of the turbine blades

We investigate the strong stabilization of a wind turbine tower model in the plane of the turbine blades, which comprises a nonuniform SCOLE system and a two-mass drive-train model (with gearbox). The control input is the torque created by the electrical generator. Using a strong stabilization theorem for a class of impedance passive linear systems with bounded control and observation operators, we show that the wind turbine tower model can be strongly stabilized. The control is by static output feedback from the angular velocities of the nacelle and the generator rotor

Floating Offshore Wind Turbines Oscillations Damping.

This article deals with the modelling and control of oscillations that appear on floating offshore wind turbines (FOWT). First, these offshore wind energy systems, located in deep waters, are described and the modeling approach is presented. Secondly, the traditional structural control strategies based on tuned mass-damper (TMD) systems for oscillations reduction are complemented with a passive mechanism called inerter in order to improve the performance of the structural controller. This work is based on a previous work by the authors in which the inerter was located in parallel to an existing TMD in the nacelle of the FOWT. In this work, the inerter is located between the tower and the barge and results are compared to those obtained previously showing better performance. The results here presented are promising in terms of oscillations damping, both in amplitude and frequency, and constitute preliminary results of the ongoing current research of the authors

Modelling and control of coupled infinite-dimensional systems

First, we consider two classes of coupled systems consisting of an infinite-dimensional part [sigma]d and a finite-dimensional part [sigma]f connected in feedback. In the first class of coupled systems, we assume that the feedthrough matrix of [sigma]f is 0 and that [sigma]d is such that it becomes well-posed and strictly proper when connected in cascade with an integrator. Under several assumptions, we derive well-posedness, regularity and exact (or approximate) controllability results for such systems on a subspace of the natural product state space. In the second class of coupled systems, [sigma]f has an invertible first component in its feedthrough matrix while [sigma]d is well-posed and strictly proper. Under similar assumptions, we obtain well-posedness, regularity and exact (or approximate) controllability results as well as exact (or approximate) observability results for this class of coupled systems on the natural state space. Second, we investigate the exact controllability of the SCOLE (NASA Spacecraft Control Laboratory Experiment) model. Using our theory for the first class of coupled systems, we show that the uniform SCOLE model is well-posed, regular and exactly controllable in arbitrarily short time when using a certain smoother state space. Third, we investigate the suppression of the vibrations of a wind turbine tower using colocated feedback to achieve strong stability. We decompose the system into a non-uniform SCOLE model describing the vibrations in the plane of the turbine axis, and another model consisting of a non-uniform SCOLE system coupled with a two-mass drive-train model (with gearbox), in the plane of the turbine blades. We show the strong stabilizability of the first tower model by colocated static output feedback. We also prove the generic exact controllability of the second tower model on a smoother state space using our theory for the second class of coupled systems, and show its generic strong stabilizability on the energy state space by colocated feedback

Boundary vibration control of a floating wind turbine system with mooring lines

In this paper, we investigate dynamic modeling, active boundary control design, and stability analysis for a coupled floating wind turbine (FWT) system, which is connected with two flexible mooring lines. It is a coupled beam-strings structure, and we design two boundary controllers to restrain the vibrations of this flexible system caused by external disturbances based on the coupled partial differential equations and ordinary differential equations (PDEs–ODEs) model. Meanwhile, significant performance of designed boundary controllers and system’s stability are theoretically analyzed, and a set of simulation results are provided to show efficacy of the proposed approach

Load reduction of a monopile wind turbine tower using optimal tuned mass dampers

We investigate to apply tuned mass dampers (TMDs) (one in the fore–aft direction, one in the side– side direction) to suppress the vibration of a monopile wind turbine tower. Using the spectral element method, we derive a finite-dimensional state-space model d from an infinite-dimensional model d of a monopile wind turbine tower stabilised by a TMD located in the nacelle. and d can be used to represent the dynamics of the tower and TMD in either the fore–aft direction or the side– side direction. The wind turbine tower subsystem of is modelled as a non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) system consisting of an Euler–Bernoulli beam equation describing the dynamics of the flexible tower and the Newton–Euler rigid body equations describing the dynamics of the heavy rotor-nacelle assembly (RNA) by neglecting any coupling with blade motions. d can be used for fast and accurate simulation for the dynamics of the wind turbine tower as well as for optimal TMD designs. We show that d agrees very well with the FAST (fatigue, aerodynamics, structures and turbulence) simulation of the NREL 5-MW wind turbine model. We optimise the parameters of the TMD by minimising the frequency-limited H2-norm of the transfer function matrix of d which has input of force and torque acting on the RNA, and output of tower-top displacement. The performances of the optimal TMDs in the fore–aft and side–side directions are tested through FAST simulations, which achieve substantial fatigue load reductions. This research also demonstrates how to optimally tune TMDs to reduce vibrations of flexible structures described by partial differential equations

Aeroelastic Performance Analysis of Wind Turbine in the Wake with a New Elastic Actuator Line Model

The scale of a wind turbine is getting larger with the development of wind energy recently. Therefore, the effect of the wind turbine blades deformation on its performances and lifespan has become obvious. In order to solve this research rapidly, a new elastic actuator line model (EALM) is proposed in this study, which is based on turbinesFoam in OpenFOAM (Open Source Field Operation and Manipulation, a free, open source computational fluid dynamics (CFD) software package released by the OpenFOAM Foundation, which was incorporated as a company limited by guarantee in England and Wales). The model combines the actuator line model (ALM) and a beam solver, which is used in the wind turbine blade design. The aeroelastic performances of the NREL (National Renewable Energy Laboratory) 5 MW wind turbine like power, thrust, and blade tip displacement are investigated. These results are compared with some research to prove the new model. Additionally, the influence caused by blade deflections on the aerodynamic performance is discussed. It is demonstrated that the tower shadow effect becomes more obvious and causes the power and thrust to get a bit lower and unsteady. Finally, this variety is analyzed in the wake of upstream wind turbine and it is found that the influence on the performance and wake flow field of downstream wind turbine becomes more serious

Stability properties of coupled impedance passive LTI systems

We study the stability of the feedback interconnection of two impedance passive linear time-invariant systems, of which one is finite-dimensional. The closed-loop system is well known to be impedance passive, but no stability properties follow from this alone. We are interested in two main issues: (1) the strong stability of the operator semigroup associated with the closed-loop system, (2) the input-output stability (meaning transfer function in H∞) of the closed-loop system. Our results are illustrated with the system obtained from the non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) model representing a vertical beam clamped at the bottom, with a rigid body having a large mass on top, connected with a trolley mounted on top of the rigid body, via a spring and a damper. Such an arrangement called a tuned mass damper (TMD), is used to stabilize tall buildings. We show that the SCOLE-TMD system is strongly stable on the energy state space and that the system is input-output stable from the horizontal force input to the horizontal velocity output

A regressive machine-learning approach to the non-linear complex FAST model for hybrid floating offshore wind turbines with integrated oscillating water columns

Offshore wind energy is getting increasing attention as a clean alternative to the currently scarce fossil fuels mainly used in Europe's electricity supply. The further development and implementation of this kind of technology will help fighting global warming, allowing a more sustainable and decarbonized power generation. In this sense, the integration of Floating Offshore Wind Turbines (FOWTs) with Oscillating Water Columns (OWCs) devices arise as a promising solution for hybrid renewable energy production. In these systems, OWC modules are employed not only for wave energy generation but also for FOWTs stabilization and cost-efficiency. Nevertheless, analyzing and understanding the aero-hydro-servo-elastic floating structure control performance composes an intricate and challenging task. Even more, given the dynamical complexity increase that involves the incorporation of OWCs within the FOWT platform. In this regard, although some time and frequency domain models have been developed, they are complex, computationally inefficient and not suitable for neither real-time nor feedback control. In this context, this work presents a novel control-oriented regressive model for hybrid FOWT-OWCs platforms. The main objective is to take advantage of the predictive and forecasting capabilities of the deep-layered artificial neural networks (ANNs), jointly with their computational simplicity, to develop a feasible control-oriented and lightweight model compared to the aforementioned complex dynamical models. In order to achieve this objective, a deep-layered ANN model has been designed and trained to match the hybrid platform's structural performance. Then, the obtained scheme has been benchmarked against standard Multisurf-Wamit-FAST 5MW FOWT output data for different challenging scenarios in order to validate the model. The results demonstrate the adequate performance and accuracy of the proposed ANN control-oriented model, providing a great alternative for complex non-linear models traditionally used and allowing the implementation of advanced control schemes in a computationally convenient, straightforward, and easy way.This work was supported in part by the Basque Government through project IT1555-22 and through the projects PID2021-123543OB-C21 and PID2021-123543OB-C22 (MCIN/AEI/10.13039/501100011033/FEDER, UE). The authors would also like to thank the UPV/EHU for the financial support through the María Zambrano grant MAZAM22/15 and Margarita Salas grant MARSA22/09 (UPV-EHU/MIU/Next Generation, EU) and through grant PIF20/299 (UPV/EHU)

Market strategies for offshore wind in Europe: A development and diffusion perspective

AbstractOffshore wind will contribute to the decarbonization of European power systems, but is currently costlier than many other generation technologies. We assess the adequacy of market strategies available to private actors developing offshore wind farms in Europe, by employing the development and diffusion pattern model. The model includes two earlier phases in addition to the large-scale deployment phase of other diffusion models: the innovation and the market adaptation phases. During its development and diffusion offshore wind moved from experimentation to a dominant design (monopile foundations and a permanent magnet generator). Simultaneously, wind farms shifted from an experimental to a commercial purpose and grew from 10 to 316MW on average. The turbine and wind farm development markets kept a high concentration throughout all phases. Also, the wind farm life cycle and supply chain became more integrated and drew less from the onshore wind and oil & gas sectors.This development and diffusion was shaped by the barriers of cost, project risk and complexity, capital requirements, and multi-disciplinarity. Wind farms developers combined three niche strategies to address these barriers: the subsidized, the geographic, and the demo, experiment and develop. The barriers make these niche strategies more adequate than strategies of mass-market (dominating a market) or wait-and-see (developing resources but waiting for uncertainty reduction before market entrance). Nonetheless, the barriers and market strategies changed during the development and diffusion pattern. Thus, cost and risk reductions decreased the importance of the subsidized niche, while the geographic niche becomes less important as offshore wind develops outside of Europe.The study also identified an increase in cooperation for wind farm development, as development became more international and with more frequent alliances. Wind farm developers and development and diffusion models research must consider how contemporary forms of cooperation improve or hinder the market strategies