Optimisation of the geometry of axisymmetric point-absorber wave energy converters

We propose a scientifically rigorous framework to find realistic optimal geometries of wave energy converters (WECs). For specificity, we assume WECs to be axisymmetric point absorbers in a monochromatic unidirectional incident wave, all within the context of linearised potential theory. We consider separately the problem of a WEC moving and extracting wave energy in heave only and then the more general case of motion and extraction in combined heave, surge and pitch. We describe the axisymmetric geometries using polynomial basis functions, allowing for discontinuities in slope. Our framework involves ensuring maximum power, specifying practical motion constraints and then minimising surface area (as a proxy for cost). The framework is robust and well-posed, and the optimisation produces feasible WEC geometries. Using the proposed framework, we develop a systematic computational and theoretical approach, and we obtain results and insights for the optimal WEC geometries. The optimisation process is sped up significantly by a new theoretical result to obtain roots of the heave resonance equation. For both the heave-only, and the heave-surge-pitch combined problems, we find that geometries which protrude outward below the waterline are generally optimal. These optimal geometries have up to 73 % less surface area and 90 % less volume than the optimal cylinders which extract the same power.

Survival probability of random walks leaping over traps

We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps of length ℓ over which the RWs can jump. We study the survival probability of such RWs when the traps are periodically distributed and separated by a distance L. We obtain exact results for the mean first-passage time and the survival probability in the special case of a double-sided exponential jump distribution. While such RWs typically survive longer than if they could not leap over traps, their survival probability still decreases exponentially with the number of steps. The decay rate of the survival probability depends in a non-trivial way on the trap length ℓ and exhibits an interesting regime when ℓ → 0 as it tends to the ratio ℓ/L, which is reminiscent of strongly chaotic deterministic systems. We generalize our model to continuous-time RWs, where we introduce a power-law distributed waiting time before each jump. In this case, we find that the survival probability decays algebraically with an exponent that is independent of the trap length. Finally, we derive the diffusive limit of our model and show that, depending on the chosen scaling, we obtain either diffusion with uniform absorption, or diffusion with periodically distributed point absorbers.

A Novel 2-D Point Absorber Numerical Modelling Method

Despite several wave energy converters (WECs) having been developed to present, no particular concept has emerged yet. The existing inventions vary significantly in terms of the operation principle and complexity of WECs. The tethered point absorbers (PAs) are among the most known devices that, thanks to their simplicity, appear to be cost-effective and reliable for offshore installation. These devices need to be advanced further and, therefore, new tailored modelling methods are required. Numerical modelling of this type of WEC has been done mainly in one degree of freedom. Existing methods for multi-degrees of freedom analysis lack pragmatism and accuracy. Nevertheless, modelling of multiple degrees of freedom is necessary for correct analysis of the device dynamic response, wave loads and device performance. Therefore, an innovative numerical method for two degrees of freedom analysis of PA WECs, which permits precisely modelling the dynamics of PA for surge and heave motions, is introduced in this paper. The new method allows assessing, in the time-domain, the dynamic response of tethered PAs using regular and irregular sea states. The novel numerical model is explained, proved and empirically validated.

Geometry Optimization of Heaving Axisymmetric Point Absorbers under Parametrical Constraints in Irregular Waves

The objective of this work is to identify the maximum absorbed power and optimal buoy geometry of a heaving axisymmetric point absorber for a given cost in different sea states. The cost of the wave energy converter is estimated as proportional to the displaced volume of the buoy, and the buoy geometry is described by the radius-to-draft ratio. A conservative wave-height-dependent motion constraint is introduced to prevent the buoy from jumping out of the free surface of waves. The constrained optimization problem is solved by a two-nested-loops method, within which a core fundamental optimization process employs the MATLAB function fmincon. Results show that the pretension of the mooring system should be as low as possible. Except for very small energy periods, the stiffness of both the power take-off and mooring system should also be as low as possible. A buoy with a small radius-to-draft ratio can absorb more power, but at the price of working in more energetic seas and oscillating at larger amplitudes. In addition, the method to choose the optimal buoy geometry at different sea states is provided.

Recent Advances in Direct-Drive Power Take-Off (DDPTO) Systems for Wave Energy Converters Based on Switched Reluctance Machines (SRM)

This chapter is focused on Power Take-Off (PTO) systems for wave energy converters (WEC), being one of the most important elements since PTOs are responsible to transform the mechanical power captured from the waves into electricity. It presents Direct-Drive PTO (DDPTO) as one of the most reliable solutions to be adapted to some particular types of WEC, such as point absorbers. A discussion about modularity and adaptability, together with intrinsic characteristics of direct-drive PTOs, is also included. Among the different technologies of electric machines that can be used in direct-drive linear PTOs, switched reluctance machines (SRM) are described in further detail. In particular, the Azimuthal Multi-translator SRM is presented as a suitable solution in order to increase power density and reduce costs. Not only the electric machine, but also the associated power electronics are described in detail. The description includes the different configurations and topologies of power converters and the most appropriate control strategies. Finally, a superconducting linear generator solution is described, presenting it as a reliable alternative for the application of direct-drive PTOs. An example of concept and preliminary design is included in order to highlight the main challenges to be faced during this process.

Numerical and Experimental Analyses on Motion Responses on Heaving Point Absorbers Connected to Large Semi-Submersibles

This study considers the motion responses of heaving point absorbers (HPAs) connected to large semi-submersibles. To analyze the motion responses for HPAs, a motion response amplitude operator (RAO) of a single HPA connected to a fixed wall was obtained in a two-dimensional wave flume. A frequency-domain eigenvalue analysis is used to evaluate the motion RAO of a single HPA, and the experimental and numerical results of motion RAO were compared. A model test was conducted to analyze the motions of multiple HPAs connected to a large semi-submersible in a 3D ocean basin. The motion RAOs of the multiple HPAs connected to the large semi-submersible were compared with the motion RAO of the single HPA connected to the fixed wall.

A Comparative Study of Model Predictive Control and Optimal Causal Control for Heaving Point Absorbers

Efforts by various researchers in recent years to design simple causal control laws that can be applied to WEC devices suggest that these controllers can yield similar levels of energy output as those of more complex non-causal controllers. However, most studies were established without adequately considering device and power conversion system constraints which are relevant design drivers from a cost and economic point of view. It is therefore imperative to understand the benefits of MPC compared to causal control from a performance and constraint handling perspective. In this paper, we compare linear MPC to a casual controller that incorporates constraint handling to benchmark its performance on a one DoF heaving point absorber in a range of wave conditions. Our analysis demonstrates that MPC provides significant performance advantages compared to an optimized causal controller, particularly if significant constraints on device motion and/or forces are imposed. We further demonstrate that distinct control performance regions can be established that correlate well with classical point absorber and volumetric limits of the wave energy conversion device.