Model predictive control of sea wave energy converters – Part II: The case of an array of devices

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Guang Li and Mike R. Belmont, Renewable Energy – August 2014

Abstract

This paper addresses model predictive control (MPC) of highly-coupled clusters of sea wave energy converters (WECs). Since each WEC is not only a wave absorber but also a wave generator, the motion of each WEC can be affected by the waves generated by its adjacent WECs when they are close to each other. A distributed MPC strategy is developed to maximize the energy output of the whole array and guarantee the safe operation of all the WECs with a reasonable computational load. The system for an array is partitioned into subsystems and each subsystem is controlled by a local MPC controller. The local MPC controllers run cooperatively by transmitting information to each other. Within one sampling period, each MPC controller performs optimizations iteratively so that a global optimization for the whole array can be approximated. The computational burden for the whole array is also distributed to the local controllers. A numerical simulation demonstrates the efficacy of the proposed control strategy. For the WECs operating under constraints explored, it is found that the optimized power output is an increasing function of degree of WEC–WEC coupling. Increases in power of up to 20% were achieved using realistic ranges of parameters with respect to the uncoupled case.

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Model predictive control of sea wave energy converters – Part I: A convex approach for the case of a single device

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Guang Li and Michael R Belmont, Renewable Energy – September 2014

Abstract

This paper investigates model predictive control (MPC) of a single sea wave energy converter (WEC). By using control schemes which constrain certain quantities, such as the maximum size of the feedback force, the energy storage for actuators and relative heave motion, it is possible for control to not only improve performance but to directly impact strongly on design and cost. Motivated by this fact, a novel objective function is adopted in the MPC design, which brings obvious benefits: First, the quadratic program (QP) derived from this objective function can be easily convexified, which facilitates the employment of existing efficient optimization algorithms. Second, this novel design can trade off the energy extraction, the energy consumed by the actuator and safe operation. Moreover, an alternative QP is also formulated with the input slew rate as optimization variable, so that the slew rate limit of an actuator can be explicitly incorporated into optimization. All these benefits promote the real-time application of MPC on a WEC and reduced cost of hardware.

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Shape design and numerical analysis on a 1 MW tidal current turbine for the south-western coast of Korea

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Patrick Mark Singh and Young-Do Choi, Renewable Energy – August 2014

Abstract

The study concentrates on the shape design and numerical analysis of a 1 MW horizontal axis tidal current turbine (HATCT), which can be applied near the southwest regions of Korea. On the basis of actual tidal current conditions of south-western region of Korea, configuration design of 1 MW class turbine rotor blade is carried out by blade element momentum theory (BEMT). The hydrodynamic performance including the lift and drag forces, is conducted with the variation of the angle of attack using an open source code of X-Foil. The optimized blade geometry is used for Computational Fluid Dynamics (CFD) analysis with hexahedral numerical grids. This study focuses on developing a new hydrofoil and designing a blade with relatively shorter chord length in contrast to a typical TCT blade. Therefore, after a thorough study of two common hydrofoils, (S814 and DU-91-W2-250, which show good performance for rough conditions), a new hydrofoil, MNU26, is developed. The new hydrofoil has a 26% thickness that can be applied throughout the blade length, giving good structural strength. Power coefficient, pressure and velocity distributions are investigated according to Tip Speed Ratio by CFD analysis. As cavitation analysis is also an important part of the study, it is investigated for all the three hydrofoils. Due to the shorter chord length of the new turbine blade in contrast to a typical TCT blade design, a Fluid Structure Interaction (FSI) analysis is also done. Concrete conclusions have been made after comparing the three hydrofoils, considering their performance, efficiency, occurrence of cavitation and structural feasibility.

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Computationally efficient modelling of dynamic soil-structure interaction of offshore wind turbines on gravity footings

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M. Damgaard, L.V. Andersen, and L.B. Ibsen – Renewable Energy, August 2014

Abstract

The formulation and quality of a computationally efficient model of offshore wind turbine surface foundations are examined. The aim is to establish a model, workable in the frequency and time domain, that can be applied in aeroelastic codes for fast and reliable evaluation of the dynamic structural response of wind turbines, in which the geometrical dissipation related to wave propagation into the subsoil is included. Based on the optimal order of a consistent lumped-parameter model obtained by the domain-transformation method and a weighted least-squares technique, the dynamic vibration response of a 5.0 MW offshore wind turbine is evaluated for different stratifications, environmental conditions and foundation geometries by the aeroelastic nonlinear multi-body code HAWC2. Analyses show that a consistent lumped-parameter model with three to five internal degrees of freedom per displacement or rotation of the foundation is necessary in order to obtain an accurate prediction of the foundation response in the frequency and time domain. In addition, the required static bearing capacity of surface foundations leads to fore–aft vibrations during normal operation of a wind turbine that are insensitive to wave propagating in the subsoil—even for soil stratifications with low cut-in frequencies. In this regard, utilising discrete second-order models for the physical interpretation of a rational filter puts special demands on the Newmark β-scheme, where the time integration in most cases only provides a causal response for constant acceleration within each time step.

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Coalesced effect of cavitation and silt erosion in hydro turbines—A review

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Pannkaj P. Gohil and R.P. Saini – Renewable and Sustainable Energy Reviews, May 2014

Abstract

Cavitation is a phenomenon which manifests itself in the pitting of the metallic surfaces of turbine parts because of the formation of cavities. However, silt erosion is caused by the dynamic action of silt flowing along with water, impacting against a solid surface. The erosion and abrasive wear not only reduce the efficiency and the life of the turbine but also cause problems in operation and maintenance, which ultimately lead to economic losses. Researchers have studied that the cavitation in silt flow is more serious than in pure water. However, the coalesced effect of silt erosion and cavitation is found to be more pronounced than their individual effects.

In the present paper the studies in this field carried out by various investigators are discussed and presented. Parameters related to the combined effect of cavitation and silt erosion which are responsible for efficiency loss due to erosion as investigated by researchers have also been discussed.

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