Stochastic Linearization of the Morison Equation Applied to an Offshore Wind Turbine

Housseine, Charaf Ouled; Monroy, Charles; Hauteclocque, Guillaume de

doi:10.1115/omae2015-41301

Cited by 10 publications

(12 citation statements)

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“…In order to obtain a suitable model for LQ controller design, the quadratic viscous drag force (per unit length) in irregular waves can be approximated using stochastic linearization. However, as pointed out by Housseine et al [23], the advantage of stochastic linearization with respect to regular wave linearization may be small in the presence of uncertainties related to the Morison equation coefficients. In this case, the hydrodynamic viscous force (per unit length) can be approximated using equivalent linearization of the quadratic drag due to floating body motions in regular waves combined with an absolute velocity approach [21].…”

Section: Hydrodynamicsmentioning

confidence: 99%

“…Assuming surge and pitch motions in a particular sea state modeled by ξ i = Ξ i cos(ωt + ε i ), i = 1, 5, respectively, the relevant quadratic drag force terms (per unit length) related to the floater motions in Morison Equation (11) can be linearized according to [23]:…”

Section: Hydrodynamicsmentioning

confidence: 99%

“…In this case, fluid memory effects (convolution integrals in the equations of motion) and radiation damping can be neglected [22]. The stochastic/equivalent linearization of the quadratic viscous damping (drag) in the Morison equation, which is necessary for the application of linear control methods, is addressed in [23] for an offshore wind turbine.…”

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confidence: 99%

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Linear Quadratic Optimal Control of a Spar-Type Floating Offshore Wind Turbine in the Presence of Turbulent Wind and Different Sea States

Ramos

2018

JMSE

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This paper presents the design of a linear quadratic (LQ) optimal controller for a spar-type floating offshore wind turbine (FOWT). The FOWT is exposed to different sea states and constant wind turbulence intensity above rated wind speed. A new LQ control objective is specified for the floater-turbine coupled control, in accordance with standard requirements, to reduce both rotor speed fluctuations and floater pitch motion in each relevant sea state compared with a baseline proportional-integral (PI) controller. The LQ weighting matrices are selected using time series of the wind/wave disturbances generated for the relevant sea states. A linearized state-space model is developed, including the floater surge/pitch motions, rotor speed, collective blade pitch actuation, and unmeasured environmental disturbances. The wind disturbance modeling is based on the Kaimal spectrum and aerodynamic thrust/torque coefficients. The wave disturbance modeling is based on the Pierson-Moskowitz spectrum and linearized Morison equation. A high-fidelity FOWT simulator is used to verify the control-oriented model. The simulation results for the OC3-Hywind FOWT subjected to turbulent wind show that a single LQ controller can yield both rotor speed fluctuation reduction of 32-72% and floater pitch motion reduction of 22-44% in moderate to very rough sea states compared with the baseline PI controller.

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Section: Hydrodynamicsmentioning

confidence: 99%

Section: Hydrodynamicsmentioning

confidence: 99%

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Linear Quadratic Optimal Control of a Spar-Type Floating Offshore Wind Turbine in the Presence of Turbulent Wind and Different Sea States

Ramos

2018

JMSE

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“…N 2 is the total number of contributing submerged panels. Further details can be found in Reference [27].…”

Section: (A) Exact Formulation Of Quadratic Drag Forcesmentioning

confidence: 99%

Numerical and Experimental Modelling of a Wave Energy Converter Pitching in Close Proximity to a Fixed Structure

Heras

Thomas

Kramer

et al. 2019

JMSE

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Free-floating bodies are commonly modelled using Cummins' equation based on linear potential flow theory and including non-linear forces when necessary. In this paper, this methodology is applied to a body pitching around a fixed hinge (not free-floating) located close to a second bottom-fixed body. Due to the configuration of the setup, strong hydrodynamic interactions occur between the two bodies. An investigation is made into which non-linear forces need to be included in the model in order to accurately represent reality without losing computational efficiency. The non-linear forces investigated include hydrostatic restoring stiffness and different formulations of excitation forces and quadratic drag forces. Based on a numerical comparison, it is concluded that the different non-linear forces, except for the quadratic drag force, have a minor influence on the calculated motion of the pitching body. Two formulations of the quadratic drag force are shown to result in similar motions, hence the most efficient one is preferred. Comparisons to wave basin experiments show that this model is, to a large extent, representative of reality. At the wave periods where the hydrodynamic interactions between the bodies are largest, however, the amplitudes of motion measured in the wave basin are lower than those calculated numerically.

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“…Non-linear hydrodynamics have been found to be negligible under some conditions [8,9], while other non-linearities are more significant but can be approximated, such as in the aerodynamic loads and the control system dynamics [10], and viscous drag forces on submerged structures (e.g. [11]). However, the conditions under which non-linearity in the structural dynamics is important have not been established.…”

Section: Introductionmentioning

confidence: 99%

Complex but negligible: Non-linearity of the inertial coupling between the platform and blades of floating wind turbines

Lupton

Langley

2019

Renewable Energy

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Approximate linearised models can be important for preliminary design of floating wind turbines, but their value depends on how well they approximate the real-world non-linear behaviour. This paper focuses on the non-linear inertial coupling between motion of the floating platform and the blade dynamics, using a simplified model to demonstrate how the inertial coupling works, and systematically studying the linearity of the dynamic blade response to different directions, amplitudes and frequencies of motion. Simplified equations of motion are derived and approximately solved analytically, showing that the blade response contains harmonics at a range of frequencies, some linear and some non-linear in the amplitude of the platform motion. Comparison to numerical simulations shows that the analytical results were qualitatively useful but inaccurate for large platform motions. Because of the multiple harmonics in the response, there are more combinations of rotor speeds and platform motions leading to large resonant blade responses and non-linear behaviour than might be expected. Overall, for realistically low rotor speeds and platform frequencies (below 20 rpm and 0.2 Hz), non-linear inertial loading due to platform motion should be negligible. The implications of this work for the use of linearised structural models and the relevance of scale model testing are discussed.

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Stochastic Linearization of the Morison Equation Applied to an Offshore Wind Turbine

Cited by 10 publications

References 0 publications

Linear Quadratic Optimal Control of a Spar-Type Floating Offshore Wind Turbine in the Presence of Turbulent Wind and Different Sea States

Linear Quadratic Optimal Control of a Spar-Type Floating Offshore Wind Turbine in the Presence of Turbulent Wind and Different Sea States

Numerical and Experimental Modelling of a Wave Energy Converter Pitching in Close Proximity to a Fixed Structure

Complex but negligible: Non-linearity of the inertial coupling between the platform and blades of floating wind turbines

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