The active control of wave energy converters with oil-hydraulic power take-off systems presents important demands on the electrical drives attached to their pumps, in particular on the required drive accelerations and rotational speeds. This work analyzes these demands on the drives and designs reliable control approaches for such drives by simulating a wave-to-wire model in a hardware in-the-loop simulation test rig. The model is based on a point absorber wave energy converter, being the wave, hydrodynamic and oil-hydraulic part simulated in a computer that sends and receives signals from the real embedded components, such as the drive generator, controller and back-to-back converter. Three different control strategies are developed and tested in this test rig and the results revealed that despite the drive limitations to acceleration levels, well above 1 x 10(4) rpm/s, these do not significantly affect the power take-off efficiency, because the required acceleration peaks rarely achieve these values. Moreover this drive is much more economical than an oil-hydraulic and equivalent one that is able to operate at those peaks of acceleration. (C) 2017 Elsevier Ltd. All rights reserved.

This paper presents a WEC-PTO mechanism interface adaptable to different sea states. The physical structure of a PTO based on oil-hydraulic transformer units is optimized in order to increase the harvested wave power of a point absorber WEC. The study includes technological constraints on the PTO, which are a minimum averaged hydraulic pressure of 170 bar and a cylinder stroke constrained to 3 m. The mechanism interface of the Wavestar prototype is used, modified and presented. A modification on the interface is proposed allowing an adaptability of the mechanism interface. The two mechanism interfaces connected to the PTO system are simulated for three different sea states conditions and the simulation results are then compared and presented. The corresponding control and geometric optimal parameters are determined with genetic algorithms. According to the results, the modified mechanism interface achieves more 242% of the average harvested power on the less energetic sea state condition when compared to the original one.

The present study takes the hydrodynamic analysis of circular array of WECs further by proposing a more detailed circular array WEC concept. Time domain simulations are performed to analyse the response of each floater in the array. The total power absorption by the array is evaluated and compared with those of linear WEC arrays. This study will help in the further evaluation of circular array of wave energy devices.

Arrays of heaving point absorbers in various arrangements are analysed to study their performance in terms of the amount of power absorption and the power uniformity among floaters. The numerical simulations for the determination of hydrodynamic coefficients and forces are obtained using a Boundary Element Method (BEM) code. A linear external damping coefficient is applied to enable power extraction and a supplementary mass is introduced to tune the floater to the incoming wave conditions. Each floater is assumed to have its own identical power take-off system. The external damping coefficient and the supplementary mass are individually optimized for each floater to maximize the total power absorption by the array. This optimization is implemented with slamming, stroke and force restrictions imposed on the floater motion by SQP method. Attention is also paid to the performance of each floater in various arrangements. Furthermore, the effect of incoming wave headings is taken into account. To quantify the performance, q-factor and coefficient of variation are compared for each array for a range of sea states. This present study will be helpful in the understanding and design of the best possible configuration of arrays of heaving point absorber WEC systems to extract more wave power and achieve better power recovery uniformity.

The behaviour of arrays of 12 heaving point absorbers in concentric arrangements is numerically assessed in a frequency domain model. The floaters are attached to a central cylindrical bottom-mounted structure. Each point absorber is restricted to the heave mode and is assumed to have its own linear power take-off system consisting of an external damping coefficient enabling power extraction and a supplementary mass coefficient tuning the point absorber to the incoming waves. The external damping and supplementary mass coefficients are optimized to maximize the power absorption by each floater in the array, with a restriction on the total control force that can be applied on the floaters. Various concentric arrangements with different radii and number of concentric circles are analysed to determine the most efficient among them. Moreover, the influence of the presence of a central bottom-mounted pillar and the effect of change in its dimension and shape on the power absorption are also studied.

The variable displacement oil-hydraulic pumps for the Power Take-Off (PTO) of wave energy converters must work above 80% of maximum displacement in order to have an overall efficiency of approximately 94.5%. This is achieved by controlling their rotational speed when the oil-hydraulic power fluctuates in time. Three speed control strategies have been presented, the first fixing the maximum possible speed in each sea state, the second by slowly varying the pump speed between speed peak values and average ones, and the third by working with highly variable speed reference values. The worst pump efficiency is achieved with the first strategy while the best one with the third strategy. However, the first has less impact than the third one in the pump lifecycle. On the other hand, the second strategy is used to make a trade-off between pump efficiency and lifecycle. However, this paper presents a fourth speed control strategy, which is a hybrid of the second and third strategies. So, the objectives of this paper were to know if these strategies are implementable in a test rig and also on a new PTO concept and determining what modifications should be introduced in these PTO strategies and hardware. This paper also contributes with the application of new methodologies in this field of research for the modelling of pump efficiency and pressure control, such as Neuro-Fuzzy modelling and Fuzzy Logic control systems.

This paper presents an improvement of a hydraulic Power Take-Off concept which uses a hydraulic transformer to store some of the wave energy into kinetic energy and then uses it to perform the reactive control of a Wave Energy Converter. This improvement was achieved with the replacement of piloted-to-close non-return valves, which rectify the bigger part of the useful wave power by sending it directly into the electrical generator station, with flow proportional valves. As revealed in this paper the use of these proportional valves solved the main difficulty of the PTO concept that was to operate with the same oil reference pressure in the pipeline, where the electrical generator station is connected, for a range of sea states. Moreover, several PTOs working at slightly different regimes, which would require different oil reference pressures to work efficiently, can be now attached on the same pipeline at the same reference pressure. The use of proportional instead of non-return valves adds approximately more 10% on the PTO overall hydraulic efficiency.

The effect of water depth on the power absorption by a single heaving point absorber wave energy converter, attached to a hydraulic power take-off system, is simulated and analysed. The wave energy flux for changing water depths is presented and the study is carried out at a location in the north-west Portuguese coast, favourable for wave power generation. This analysis is based on a procedure to modify the wave spectrum as the water depth reduces, namely, the TMA spectrum (Transformation spectrum). The present study deals with the effect of water depth on the spectral shape and significant wave heights. The reactive control strategy, which includes an external damping coefficient and a negative spring term, is used to maximize power absorption by the wave energy converter. The presented work can be used for making decisions regarding the best water depth for the installation of point absorber wave energy converters in the Portuguese nearshore.

The objective of this paper is to present a Power Take-Off concept to increase the wave power harvested by a point absorber Wave Energy Converter. This is achieved by increasing the maximum admissible force supported by oil-hydraulic cylinders, by arranging them in a reciprocating way. This paper presents the simulation results achieved with this cylinder arrangement and for a set of eleven standard cylinders with different piston sizes and admissible forces and compares those to the state-of-the-art cylinder design. According to the numerical results the gain on produced power with this approach depends on the cylinder piston size and sea state and it can be 1.2 to 2.2 times the power produced by the state-of-the-art design. This study also indicates that better power gains might be achieved by optimizing the reciprocating cylinder geometric layout and performing an adequate sizing of all hydraulic components in order to adapt the Power Take-Off design to these new and higher levels of harvested power.

The arrays of heaving point absorbers in both linear and circular arrangements are analysed to understand the performance of the point absorbers in absorption of wave energy for different arrangements. The hydrodynamic performance of the heaving point absorbers are studied for three different floater shapes. The floater shapes namely hemisphere-cylinder, cone-cylinder and hemisphere are considered to analyse the effect of change in shape of the floaters in the performance of wave power extraction. The numerical simulations for the determination of hydrodynamic forces and coefficients are obtained using WAMIT. The efficiency of power absorption in irregular waves is examined for different arrays of the floater configuration. In addition the floater size, shapes, draft, wave heading angle and positioning of the floaters are also analysed. The study will be helpful in the design and analysis of best possible arrangement of the array of point absorbers for wave power absorption. linear generators are currently being studied and developed and among them two promising technologies have already reached an advanced development stage such as the Archimedes Wave Swing (AWS) device, developed by the company AWS Ocean Energy and the Sea Based wave energy converter developed by the Swedish Centre for Renewable Electric Energy Conversion. The point absorbers can also operate in arrays to produce considerable amounts of power from ocean waves similar to wind energy farms (Guedes Soares et al. 2014). The array of point absorber devices under development consist of a large structure containing multiple closely spaced oscillating bodies such as Wave Star, Manchester Bobber and FO3. Several theoretical models were developed by researchers in order to deal with the waves and interacting bodies. Budal (1977), Evans (1980) and Falnes (1980) adopted the point absorber approximation to derive the expressions for the maximum power for an array of point absorbers to absorb wave energy. The approximation relies on the assumption that the bodies are small compared to the incident wave lengths so that the wave scattering within the array can be neglected while calculating the interactions. A theory accounting more accurately for the wave body interactions is the plane wave approximation which is based on the assumption that the bodies are widely spaced relative to the incident wavelengths, so that the radiated and circular scattered waves can be locally approximated by plane waves (see Simon (1982), McIver (1984), McIver and Evans (1984)). This theory is not suitable for the closely spaced bodies as the wide spacing requirement is not fulfilled except for very short wave lengths. In the majority of studies, both theories have been applied to arrays for unconstrained conditions. Contrary to the point absorber approximation, the plane wave approximation is also suitable to study the power absorption of an array in sub-optimal conditions, as scattering might be relatively important in that case. Mavrakos (1991) analysed the hydrodynamic coefficients for the groups of interacting vertical axisymmetric bodies and the theory developed is extensively compared with the point absorber approximation theory and plane wave approximation theory. McIver (1994) studied the heaving point absorbers with constraint displacements by means of the plane wave approximation. McIver et al. (1995) also studied array interactions in irregular unidirectional and directionally spread seas for a varying number of oscillators. The study suggested that the motion restrictions significantly reduce the power absorption capability of the array for longer wave lengths. Marvrakos and Kalofonos (1997) performed the study of the power absorption by arrays of vertical axisymmetric wave energy device. The evaluation of the optimum wave-power absorption characteristics of arrays of interacting wave-energy devices is analysed and the method is based on single-body hydrodynamic characteristics. Marvrakos and McIver (1997) presented a brief comparison of the methods for computing hydrodynamic characteristics of arrays of wave power devices. Ricci et al. (2007) compared results obtained with a BEM code to the point absorber approximation and optimized the point absorber geometry and inter body distance of two array configurations each consisting of five floaters in irregular waves. Thomas et al. (2008) performed a brief comparison of the numerical and experimental results for the response of the array of heaving floaters. Taghipour et al. (2008) investigated the interaction of multi-body heaving point absorbers in a floating platform in multi directional waves using mode expansion method. In the present study, the performance of the multiple point absorbers in capturing wave energy are analysed for both linear and circular arrangements of floaters. Three floater shapes are considered to analyse the performance of array of heaving point absorbers. The numerical results for the hydrodynamic coefficients for various floater shapes and power absorption for the three different arrangements are calculated and presented. In addition the results obtained for both linear and circular configurations are compared with the result as in Backer et al. (2009). 2 NUMERICAL MODELLING 2.1 Geometry Description Three floater shapes are considered to study the effect of change in shape on the wave power extraction namely a hemisphere-cylinder floater, a conecylinder floater with cone having an apex angle of 90° and a hemisphere floater, each with a base radius of 2.5 m and the extended cylindrical part of 0.5 m as shown in Figs. 1(a-c).

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