Performance investigation of a two-raft-type wave energy converter with hydraulic power take-off unit

Raft-type wave energy converter (WEC) is a multi-mode wave energy conversion device, using the relative pitch motion to drive its hydraulic power take-off (PTO) units for capturing energy from the ocean waves. The hydraulic PTO unit as its energy conversion module plays a significant role in storing large qualities of energy and making the output power smooth. However, most of the previous investigations on the raft-type WECs treat the hydraulic PTO unit as a linear PTO unit and do not consider the dynamics of the hydraulic circuit and components in their investigations. This paper is related to a two-raft-type WEC consisting of two hinged rafts and a hydraulic PTO unit. The aim of this paper is to make an understanding of the dynamics of the hydraulic PTO unit and how these affect the performance of the two-raft-type WEC. Therefore, a combined hydrodynamic and hydraulic PTO unit model is proposed to investigate and optimize the performance of the two-raft-type WEC; and based on the simulation of the combined model, the relationships between the optimal power capture ability, the optimal magnitude of the hydraulic PTO force and the wave states are numerically revealed. Results show that an approximately square wave type hydraulic PTO force is produced by the hydraulic PTO unit, which causes the performance of the two-raft-type WEC not to be sinusoidal and the energy capturing manner different from that of the device using a linear PTO unit; moreover, there is an optimal magnitude of the hydraulic PTO force for obtaining an optimal power capture ability, which can be achieved by adjusting the parameters of the hydraulic PTO unit; in regular waves, the optimal power capture ability as well as the optimal magnitude of the hydraulic PTO force normalized by the wave height presents little relationship with the wave height, mainly depends on the wave period; in irregular waves, the trends of the optimal power capture ability and the normalized optimal magnitude of the hydraulic PTO force against the peak wave periods at different significant wave heights are generally identical and show a good correlation. All means that the hydraulic PTO unit of the two-raft-type WEC can be tuned to the wave states, and these would provide a valuable guidance for the optimal design of its hydraulic PTO unit.     

Design of a hydraulic power take-off system for the wave energy device with an inverse pendulum

This paper describes a dual-stroke acting hydraulic power take-off （PTO） system employed in the wave energy converter （WEC） with an inverse pendulum. The hydraulic PTO converts slow irregular reciprocating wave motions to relatively smooth, fast rotation of an electrical generator. The design of the hydraulic PTO system and its control are critical to maximize the generated power. A time domain simulation study and the laboratory experiment of the full-scale beach test are presented. The results of the simulation and laboratory experiments including their comparison at full-scale are also presented, which have validated the rationality of the design and the reliability of some key components of the prototype of the WEC with an inverse pendulum with the dual-stroke acting hydraulic PTO system.     

垂荡式波浪能装置运动模型数值分析

垂荡式波浪能装置在海洋可再生能源开发中被广泛应用,通过浮子与摇杆在垂荡方向的相对运动吸收波浪能。在以往相关的运动预报数值分析中,通常基于微幅波假设,仅考虑浮子与摇杆在垂荡方向的运动,忽略摇杆其他自由度运动。建立并求解了垂荡式波浪能装置的非线性联合运动方程组,分析垂荡式波浪能装置的波浪载荷、浮子与平台连接处的受力情况。数值计算系统的运动响应,并将计算结果与已有的试验数据进行比较验证,结果表明数值模拟的垂荡式波能装置的运动响应与试验结果相符合。最后,应用本计算方法分析PTO(power take-off)参数对波能装置发电性能的影响。     

Dynamic analysis of wave energy converter by incorporating the effect of hydraulic transmission lines

A heaving-buoy wave energy converter equipped with hydraulic power take-off is studied in this paper. This wave energy converter system is divided into five subsystems: a heaving buoy, hydraulic pump, pipelines, non-return check valves and a hydraulic motor combined with an electric generator. A dynamic model was developed by considering the interactions between the subsystems in a state space form. The transient pressures caused by starting/stopping the buoy or closing/opening the check valves were predicted numerically using the established model. The simulation results show that transmission line dynamics play a dominant role in the studied wave energy converter system. The length of the pipeline will not only affect the amplitude of the transient pressures but also affect the converted power. The variation of the time-averaged converted electric power with the pipeline length is estimated using the simulation method for the buoy exposed to one irregular sea state. Finally, it is suggested how reduced power efficiency due to the pipelines may be ameliorated.     

Stochastic control of wave energy converters with constrained displacements for optimal power absorption

An semi-analytical solution is derived for the optimal control of the power take-off of a single-degree of freedom heave point absorber with constraints on the displacement. At first the control force is derived during states, where the displacement constraint is active. This results in an open-loop control law dependent on the external wave load on the absorber. Next, the analytical solution for the optimal control in the unconstrained state is indicated, which turns out to be of the closed loop type with feedback from the present displacement and acceleration and from future velocities. The derived control law contains an undetermined constant, which is calibrated at the interface to the previous constrained state. The approach requires the estimation of the wave load during the constrained states, and the prediction of the future velocity response during unconstrained states. An algorithm has been devised in the paper for handling these problems. The theory has been validated against numerical solutions obtained by nonlinear programming.     

Wave tank and bench-top control testing of a wave energy converter

An increasing number of experiments are being conducted to study the design and performance of wave energy converters. Often in these tests, a real-time realization of prospective control algorithms is applied in order to assess and optimize energy absorption as well as other factors. This paper details the design and execution of an experiment for evaluating the capability of a model-scale WEC to execute basic control algorithms. Model-scale hardware, system, and experimental design are considered, with a focus on providing an experimental setup capable of meeting the dynamic requirements of a control system. To more efficiently execute such tests, a dry bench testing method is proposed and utilized to allow for controller tuning and to give an initial assessment of controller performance; this is followed by wave tank testing. The trends from the dry bench test and wave tank test results show good agreement with theory and confirm the ability of a relatively simple feedback controller to substantially improve energy absorption. Additionally, the dry bench testing approach is shown to be an effective and efficient means of designing and testing both controllers and actuator systems for wave energy converters.     

Stochastic control of wave energy converters for optimal power absorption with constrained control force

This paper presents an analytical solution derived for optimal control of the power take-off of a single-degree of freedom heave point absorber with constraints on the control force. The optimal control law turns out to be noncausal with a functional dependence on future velocities. To handle this problem, an algorithm for predicting future velocities is derived. Based on the solution the mean (time-averaged) absorbed power in a given sea-state is calculated. The performance of the indicated controller in terms of the mean absorbed power is close to the optimal value obtained by nonlinear programming and better than a controller with feedback from the present displacement, velocity and acceleration, and with optimized gain factors.     

Wave climate scatter performance of a cycloidal wave energy converter

A lift based cycloidal wave energy converter (WEC) was investigated using potential flow numerical simulations in combination with viscous loss estimates based on published hydrofoil data. This type of wave energy converter consists of a shaft with one or more hydrofoils attached eccentrically at a radius. The main shaft is aligned parallel to the wave crests and submerged at a fixed depth. The operation of the WEC as a wave-to-shaft energy converter interacting with straight crested waves was estimated for an actual ocean wave climate. The climate chosen was the climate recorded by a buoy off the north-east shore of Oahu/Hawaii, which was a typical moderate wave climate featuring an average annual wave power P_W = 17 kWh/m of wave crest. The impact of the design variables radius, chord, span and maximum generator power on the average annual shaft energy yield, capacity factor and power production time fraction were explored. In the selected wave climate, a radius R = 5 m, chord C = 5 m and span of S = 60 m along with a maximum generator power of P_G = 1.25 MW were found to be optimal in terms of annual shaft energy yield. At the design point, the CycWEC achieved a wave-to-shaft power efficiency of 70%. In the annual average, 40% of the incoming wave energy was converted to shaft energy, and a capacity factor of 42% was achieved. These numbers exceeded the typical performance of competing renewables like wind power, and demonstrated that the WEC was able to convert wave energy to shaft energy efficiently for a range of wave periods and wave heights as encountered in a typical wave climate.     

Investigation on the energy absorption performance of a fixed-bottom pressure-differential wave energy converter

In this article, we investigate the energy absorption performance of a fixed-bottom pressure-differential wave energy converter. Two versions of the technology are considered: one has the moving surfaces on the bottom of the air chambers whereas the other has the moving surfaces on the top. We developed numerical models in the frequency domain, thereby enabling the power absorption of the two versions of the device to be assessed. It is observed that the moving surfaces on the top allow for easier tuning of the natural period of the system. Taking into account stroke limitations, the design is optimized. Results indicate that the pressure-differential wave energy converter is a highly efficient technology both with respect to energy absorption and selected economic performance indicators.     

Phase control through load control of oscillating-body wave energy converters with hydraulic PTO system

Oscillating bodies constitute an important class of wave energy converters, especially for offshore deployment. Phase control by latching has been proposed in the 1970s to enhance the wave energy absorption by oscillating bodies (especially the so-called point absorbers). Although this has been shown to be potentially capable of substantially increasing the amount of absorbed energy, the practical implementation in real irregular waves of optimum phase control has met with theoretical and practical difficulties that have not been satisfactorily overcome. The present paper addresses the case of oscillating-body converters equipped with a high-pressure hydraulic power take-off mechanism (PTO) that provides a natural way of achieving latching: the body remains stationary for as long as the hydrodynamic forces on its wetted surface are unable to overcome the resisting force (gas pressure difference times cross-sectional area of the ram) introduced by the hydraulic PTO system. A method of achieving sub-optimal phase-control is developed, based on the theoretical time-domain modelling of a single-degree of freedom oscillating body in regular and irregular waves, by adequately delaying the release of the body in order to approximately bring into phase the body velocity and the diffraction (or excitation) force on the body, and in this way get closer to the well-known optimal condition derived from frequency-domain analysis for an oscillating body in regular waves.     

Research on energy conversion system of floating wave energy converter

A wave power device includes an energy harvesting system and a power take-off system. The power take-off system of a floating wave energy device is the key that converts wave energy into other forms. A set of hydraulic power take-off system, which suits for the floating wave energy devices, includes hydraulic system and power generation system. The hydraulic control system uses a special“self-hydraulic control system”to control hydraulic system to release or save energy under the maximum and the minimum pressures. The maximum pressure is enhanced to 23 MPa, the minimum to 9 MPa. Quite a few experiments show that the recent hydraulic system is evidently improved in efficiency and reliability than our previous one, that is expected to be great significant in the research and development of our prototype about wave energy conversion.     

Experimental and theoretical study of a cylindrical oscillating water column device with a quadratic power take-off model

The wave power extraction by a cylindrical oscillating water column (OWC) device with a quadratic power take-off (PTO) model was studied experimentally and theoretically. In the experiment, a scaled model OWC was tested in a wave flume, with an orifice being used to simulate a quadratic PTO mechanism. In the theoretical analysis, the quadratic PTO model was linearized based on Lorenz's principle of equivalent work, which allows us to perform a frequency domain analysis using an eigen-function matching method. The effects of higher harmonic components and the spatial non-uniformity of the surface velocity inside the chamber were discussed. A semi-analytical model was proposed to understand the viscous loss affecting the measured capture length. Our treatment of the quadratic PTO model was validated by comparing quasi-linear theoretical capture length and the laboratory measurement. Our results also showed that the effects of spatial non-uniformity and viscous loss could be noticeable for shorter waves.     

Experimental and numerical investigation of non-predictive phase-control strategies for a point-absorbing wave energy converter

Phase control may substantially increase the power absorption in point-absorber wave energy converters. This study deals with validation of dynamic models and latching control algorithms for an oscillating water column (OWC) inside a fixed vertical tube of small circular cross-section by small-scale testing. The paper describes experimental and numerical results for the system's dynamics, using simple and practical latching control techniques that do not require the prediction of waves or wave forces, and which will be relevant to any type of point-absorbing devices.In the experimental set-up, the upper end of the tube was equipped with an outlet duct and a shut-off valve, which could be controlled to give a latching of the inner free surface movement. The pressure drop through the open valve is used as a simplified measure of the energy extraction. The control was realized by using the real-time measurement signals for the inner and outer surface displacement.A mathematical model of the system was established and applied in numerical simulation. In the case the OWC's diameter is much smaller than the wavelength and the wave amplitude much smaller than the draft, the free surface movement inside the tube can be described as an oscillating weightless piston. For this hydrodynamic problem an analytical solution is known. In addition, the mathematical model includes the effects of viscous flow losses, the air compressibility inside the chamber and the pressure drop across the valve. Experimental results were used to calibrate some of the model parameters, and the total model was formulated as a coupled system of six non-linear, first-order differential equations. Time-domain integration was used to simulate the system in order to test the control strategies and compare with experimental results.     

Constrained near-optimal control of a wave energy converter in three oscillation modes

This paper investigates the performance of a small axisymmetric buoy under wave-by-wave near optimal control in surge, heave, and pitch modes in long-crested irregular waves. Wave prediction is obtained using a deterministic propagation model. The paper describes the overall formulation leading up to the derivation of the feedforward control forces in surge and heave, and the control moment in pitch. The radiation coupling between surge and pitch modes is accounted for in the model. Actuation is relative to deeply submerged reaction masses. Heave oscillations are constrained by the swept-volume limit. Oscillation constraints are also applied on the surge and pitch oscillations. The paper discusses time-domain simulations for an irregular wave input with and without the present control. Also discussed are results obtained over a range of irregular wave conditions derived for energy periods from 7 s to 17 s, and a significant wave height of 1 m. It is found that, while the gains in power capture enabled by the present control are significant, the actuation forces are also very large, given the small size of the buoy. Further, due to the small size, heave is found to be the dominant contributor to power capture, with relatively modest contributions from surge and pitch.     

Design pressure distributions on the hull of the FLOW wave energy converter

This paper presents a procedure to calculate the design pressure distributions on the hull of a wave energy converter (WEC). Design pressures are the maximum pressure values that the device is expected to experience during its operational life time. The procedure is applied to the prototype under development by Martifer Energy (FLOW—Future Life in Ocean Waves).A boundary integral method is used to solve the hydrodynamic problem. The hydrodynamic pressures are combined with the hydrostatic ones and the internal pressures of the large ballast tanks. The first step consists of validating the numerical results of motions by comparison with measured experimental data obtained with a scaled model of the WEC. The numerical model is tuned by adjusting the damping of the device rotational motions and the equivalent damping and stiffness of the power take-off system. The pressure distributions are calculated for all irregular sea states representative of the Portuguese Pilot Zone where the prototype will be installed and a long term distribution method is used to calculate the expected maximum pressures on the hull corresponding to the 100-year return period.     

Estimating the potential of ocean wave power resources

The realistic assessment of an ocean wave energy resource that can be converted to an electrical power at various offshore sites depends upon many factors, and these include estimating the resource recognizing the random nature of the site-specific wave field, and optimizing the power conversion from particular wave energy conversion devices. In order to better account for the uncertainty in wave power resource estimates, conditional probability distribution functions of wave power in a given sea-state are derived. Theoretical expressions for the deep and shallow water limits are derived and the role of spectral width is studied. The theoretical model estimates were compared with the statistics obtained from the wave-by-wave analysis of JONSWAP based ocean wave time-series. It was shown that the narrow-band approximation is appropriate when the variability due to wave period is negligible. The application of the short-term models in evaluating the long-term wave power resource at a site was illustrated using wave data measured off the California coast. The final example illustrates the procedure for incorporating the local wave data and the sea-state model together with a wave energy device to obtain an estimate of the potential wave energy that could be converted into a usable energy resource.     

A second order random wave model for predicting the power performances of a wave energy converter

The power performances of a point absorber wave energy converter(WEC) operating in a nonlinear multidirectional random sea are rigorously investigated. The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter. This is a new approach, and, as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea, avoids the inaccuracies resulting from using a first order linear wave model in the simulation process. The predicted results have been systematically analyzed and compared, and the advantages of using this new approach have been convincingly substantiated.     

The effect of water depth on the performance of a small surging wave energy converter

The effect of water depth on the performance of a small surging wave energy converter (WEC) is investigated analytically, numerically and experimentally. It is shown that although the average annual incident wave power is significantly reduced by water depth, a large proportion of this reduction is due to the dissipation of highly energetic, but largely unexploitable seas. It is also shown that the power capture is related more closely to incident wave force than incident wave power. Experimental results demonstrate that both the surge wave force and power capture of a flap-type WEC increase in shallow water.     

Large capacity multi-float configurations for the wave energy converter M4 using a time-domain linear diffraction model

The moored three-float line absorber WEC M4 has been developed to optimise power capture through experiments and linear diffraction modelling. With the progression down wave from small to medium to large floats, the device heads naturally into the wave direction. The bow and mid floats are rigidly connected by a beam and a beam from the stern float is connected to the hinge point above the mid float for power take off (PTO). Increasing the bow to mid float spacing to be more than 50% greater than the mid to stern float spacing has been found to improve power capture. To increase power capture further and potentially reduce electricity generation cost the number of mid floats and stern floats is increased while maintaining a single bow float for mooring connection. The bow and mid floats still form a rigid body while the stern floats may respond independently. A time domain linear diffraction model based on Cummins method has been applied to configurations of 121, 123, 132, 133, and 134 floats where the numbers indicate the number of floats: bow, mid, stern. This shows how power capture is increased while response remains similar. We only consider uni-directional (long-crested) waves with narrow band width typical of swell. By considering scatter diagrams for various offshore sites capacities may range from 3.7 MW to 17.3 MW for the eight float system with a capacity factor of 1/3 while the cost of electricity assuming capital cost to be a fixed multiple of steel cost is reduced from that for the three-float system.