Tag Archives: Optimization

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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Reliability-Based Structural Optimization of Wave Energy Converters


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Simon Ambühl, Morten Kramer and John Dalsgaard Sørensen – Energies, December 2014

Abstract

More and more wave energy converter (WEC) concepts are reaching prototype level. Once the prototype level is reached, the next step in order to further decrease the levelized cost of energy (LCOE) is optimizing the overall system with a focus on structural and maintenance (inspection) costs, as well as on the harvested power from the waves.  Continue reading

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Tidal turbine array optimisation using the adjoint approach


S.W. Funke, P.E. Farrell, and M.D. Piggott – Renewable Energy, March 2014

Abstract

Oceanic tides have the potential to yield a vast amount of renewable energy. Tidal stream generators are one of the key technologies for extracting and harnessing this potential. In order to extract an economically useful amount of power, hundreds of tidal turbines must typically be deployed in an array. This naturally leads to the question of how these turbines should be configured to extract the maximum possible power: the positioning and the individual tuning of the turbines could significantly influence the extracted power, and hence is of major economic interest. However, manual optimisation is difficult due to legal site constraints, nonlinear interactions of the turbine wakes, and the cubic dependence of the power on the flow speed. Continue reading

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A coupled hydro-structural design optimization for hydrokinetic turbines


Nitin Kolekar and Arindam Banerjee – Journal of Renewable and Sustainable Energy, October 2013

Abstract

An optimization methodology for a stall regulated, fixed pitch, horizontal axis hydrokinetic turbine is presented using a combination of a coupled hydro-structural analysis and Genetic Algorithm (GA) based optimization method. Design and analysis is presented for two different designs: a constant chord, zero twist blade, and a variable chord, twisted blade. A hybrid approach is presented combining Blade Element Momentum (BEM), GA, Computational Fluid Dynamics (CFD), and Finite Element Analysis (FEA) techniques. Continue reading

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The automation of PDE-constrained optimisation and its applications


Simon Funke, Doctoral Dissertation, Imperial College, UK, 2013

Abstract

This thesis is concerned with the automation of solving optimisation problems constrained by partial differential equations (PDEs). Gradient-based optimisation algorithms are the key to solve optimisation problems of practical interest. The required derivatives can be efficiently computed with the adjoint approach. However, current methods for the development of adjoint models often require a significant amount of effort and expertise, in particular for non-linear time-dependent problems. This work presents a new high-level reinterpretation of algorithmic differentiation to develop adjoint models. This reinterpretation considers the discrete system as a sequence of equation solves. Applying this approach to a general finite-element framework results in an automatic and robust way of deriving and solving adjoint models. Continue reading

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Modelling and geometry optimisation of wave energy converters


Adi Kurniawan – NTNU, Doctoral Dissertation, April 2013

Abstract

The ultimate goal of wave energy undertaking is to find a solution that minimises the cost of delivered energy. Not only should a device maximise its energy absorption, but also the costs associated with absorbing and converting that energy into useful forms should be minimised. Towards realising this goal, this thesis contributes in three main areas, namely, numerical modelling, geometry optimisation, and geometry control.

The highlights of numerical modelling include the use of bond graph—a domain-independent, graphical representation of dynamical systems—in developing numerical models of wave energy converters (WECs), and the use of state-space models to represent the wave radiation terms. It is shown that bond graph is well-suited for modelling WECs, which involve interactions between multiple energy domains, and that state-space models of the wave radiation terms are efficient and sufficiently accurate for use in time-domain simulations of WECs. Both bond graph and state-space models are used in the modelling of a floating oscillating water column device, which, from the point of view of hydrodynamics, is a complex device involving various hydrodynamic radiation terms. Continue reading

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Optimal design of a tidal turbine


J.L. Kueny, T. Lalande, J.J. Herou and L. Terme – IOP Conference Series: Earth and Environmental Science, 2012

Abstract

An optimal design procedure has been applied to improve the design of an open-center tidal turbine. A specific software developed in C++ enables to generate the geometry adapted to the specific constraints imposed to this machine. Automatic scripts based on the AUTOGRID, IGG, FINE/TURBO and CFView software of the NUMECA CFD suite are used to evaluate all the candidate geometries. This package is coupled with the optimization software EASY, which is based on an evolutionary strategy completed by an artificial neural network. A new technique is proposed to guarantee the robustness of the mesh in the whole range of the design parameters. An important improvement of the initial geometry has been obtained. To limit the whole CPU time necessary for this optimization process, the geometry of the tidal turbine has been considered as axisymmetric, with a uniform upstream velocity. A more complete model (12 M nodes) has been built in order to analyze the effects related to the sea bed boundary layer, the proximity of the sea surface, the presence of an important triangular basement supporting the turbine and a possible incidence of the upstream velocity.

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The multi-objective optimization of the horizontal-axis marine current turbine based on NSGA-II algorithm


G.J. Zhu, P.C. Guo, X.Q. Luo and J.J. Feng – IOP Conference Series: Earth and Environmental Science, 2012

Abstract

The present paper describes a hydrodynamic optimization technique for horizontal-axial marine current turbine. The pitch angle distribution is important to marine current turbine. In this paper, the pitch angle distribution curve is parameterized as four control points by Bezier curve method. The coordinates of the four control points are chosen as optimization variables, and the sample space are structured according to the Box-Behnken experimental design method (BBD). Then the power capture coefficient and axial thrust coefficient in design tip-speed ratio is obtained for all the elements in the sample space by CFD numerical simulation. The power capture coefficient and axial thrust are chosen as objective function, and quadratic polynomial regression equations are constructed to fit the relationship between the optimization variables and each objective function according to response surface model. With the obtained quadratic polynomial regression equations as performance prediction model, the marine current turbine is optimized using the NSGA-II multi-objective genetic algorithm, which finally offers an improved marine current turbine.

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Constrained optimization of the shape of a wave energy collector by genetic algorithm


A.P. McCabe – Renewable Energy, March, 2013

Abstract

Wave energy extraction requires the conversion of the energy within the waves to drive the power take off system, often by means of a principal interface, or collector. This paper describes part of the development of a robust, systematic method of optimizing the collector shape to improve energy extraction using a genetic algorithm. The collector geometry uses a parametric description based upon bi-cubic B-spline surfaces, generated from a relatively small number of control points to reduce the dimensionality of the search space. The collector shapes that are optimized have one plane of symmetry and move in one degree of freedom (surge). Each candidate shape is assessed in a wave climate based upon data from a site in the North-East Atlantic Ocean. Three cost functions, distinguished by the severity of the penalty put on the size of the candidate collectors, and four constraint regimes, defined by two displacement and two power rating limits, are the governing influences on the twelve optimization procedures described. The selected collector shapes from each optimization run are appraised in terms of size, complexity and their performance compared to that of ‘benchmark’ box-shaped collectors.

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