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.     

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.     

双浮子点吸收式波能转换装置参数研究

点吸收式波能转换装置是具有较好应用前景的一种波浪能开发利用装置,其参数设计直接影响到波浪能开发利用的可行性与有效性.作者针对青岛斋堂岛目标海域海况,通过数值模拟首先应用单因素敏感性分析法分析了双浮子点吸收式波能转换装置的结构尺寸、锚固形式、波流夹角、PTO阻尼、PTO刚度等参数对装置俘能功率的独立影响规律.之后考虑多参...     

Declutching control of a wave energy converter

When hydraulic power take off (PTO) is used to convert the mechanical energy of a wave energy converter (WEC) into a more useful form of energy, the PTO force needs to be controlled. Continuous controlled variation of the PTO force can be approximated by a set of discrete values. This can be implemented using either variable displacement pumps or several hydraulic cylinders or several high pressure accumulators with different pressure levels. This pseudo-continuous control could lead to a complex PTO with a lot of components. A simpler way for controlling this hydraulic PTO is declutching control, which consists in switching on and off alternatively the wave energy converter's PTO. This can be achieved practically using a simple by-pass valve. In this paper, the control law of the valve is determined by using the optimal command theory. It is shown that, theoretically when considering a wave activated body type of WEC, declutching control can lead to energy absorption performance at least equivalent to that of pseudo-continuous control. The method is then applied to the case of the SEAREV wave energy converter, and it is shown than declutching control can even lead to a higher energy absorption, both in regular and irregular waves.     

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.     

OWC wave energy devices with air flow control

A theoretical model is developed to simulate the energy conversion, from wave to turbine shaft, of an oscillating-water-column (OWC) plant equipped with a Wells air-turbine and with a valve (in series or in parallel with the turbine) for air-flow control. Numerical simulations show that the use of a control valve, by preventing or reducing the aerodynamic stall losses at the turbine rotor blades, may provide a way of substantially increasing the amount of energy produced by the plant, particularly at the higher incident wave power levels. From the hydrodynamic point of view, a by-pass valve or a throttle valve should be used depending on whether the wave energy absorbing system is over-damped or under-damped by the turbine.     

Absorption of wave energy by elongated bodies

Slender-body approximations are used to predict the maximum rate of energy absorption by an elongated floating vessel which performs vertical motions of varying amplitude and phase along its length. Simple estimates are derived for the amplitude and phase of particular mode shapes, and for the corresponding power absorption. Specific mode shapes considered include polynomials, trigonometric functions, and piecewise-linear functions intended to represent an articulated raft. An articulated raft with two hinges appears to be optimum from the engineering standpoint.     

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.     

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.     

Near-optimal control of a wave energy device in irregular waves with deterministic-model driven incident wave prediction

This paper investigates wave-by-wave control of a wave energy converter using incident wave prediction based on up-wave surface elevation measurement. The goal of control is to approach the hydrodynamically optimum velocity leading to optimum power absorption. This work aims to study the gains in energy conversion from a deterministic wave propagation model that accounts for a range of group velocities in deriving the prediction. The up-wave measurement distance is assumed to be small enough to allow a deterministic propagation model, and further, both wave propagation and device response are assumed to be linear. For deep water conditions and long-crested waves, the propagation process is also described using an impulse response function (e.g. [1]). Approximate low and high frequency limits for realistic band-limited spectra are used to compute the corresponding group velocity limits. The prediction time into the future is based on the device impulse response function needed for the evaluation of the control force. The up-wave distance and the duration of measurement are then determined using the group velocity limits above.A 2-body axisymmetric heaving device is considered, for which power capture is through the relative heave oscillation between the two co-axial bodies. The power take-off is assumed to be linear and ideal as well as capable of applying the necessary resistive and reactive load components on the relative heave oscillation. The predicted wave profile is used along with device impulse response functions to compute the actuator force components at each instant. Calculations are carried out in irregular waves generated using a number of uni-modal wave spectra over a range of energy periods and significant wave heights. Results are compared with previous studies based on the use of instantaneous up-wave wave-profile measurements, both without and with oscillation constraints imposed. Considerable improvements in power capture are observed with the present approach over the range of wave conditions studied.     

有效吸收和传递波浪能的锚泊系统的设计制作

将传统定位浮标加以改进,可以形成一种能有效吸收和传递波浪能的锚泊系统。此系统的最上端是漂浮着的海面浮标,海面浮标下端连着锚泊钢缆,锚泊钢缆下端到海底之间又依次连有张紧锤、储链和重物锚块。锚泊系统中的海面浮标随波浪同步上下起伏,从而带动与其连在一起的由张紧锤绷直的锚泊钢缆上下振动,于是海面浮标吸收波浪能并由引导缆向下传递。20 m长的储链可以保证整个装置在涨潮、退潮的极限水深情况下,仍旧可以有效地传递海表面波浪能;合适的重物锚块可以起到为整个系统定位的功能。最后给出了一个实际应用波浪能的例子。设计制作的锚泊系统可以有效吸收和传递波浪能,为波浪能的利用提供了一种行之有效的方法。     

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.     

Optimal causal control of a wave energy converter in a random sea

This paper concerns the design of feedback control systems to maximize power generation of a wave energy converter (WEC) in a random sea. In the literature on WEC control, most of the proposed feedback controllers fall into three categories. Many are static; i.e., they extract power by imposing an equivalent damping or resistive load on the power take-off (PTO) devices. Others are dynamic and are designed to maximize power generation at all frequencies, which results in an anticausal feedback law. Other dynamic control design methods are causal, and are tuned to achieve the anticausal performance at only a single frequency. By contrast, this paper illustrates that the determination of the true optimal causal dynamic controller for a WEC can be found as the solution to a nonstandard linear quadratic Gaussian (LQG) optimal control problem. The theory assumes that the control system must make power generation decisions based only on present and past measurements of the generator voltages and/or velocities. It is shown that unlike optimal anticausal control, optimal causal control requires knowledge of the stationary spectral characteristics of the random sea state. Additionally, it is shown that the efficiency of the generator factors into the feedback synthesis. The theory is illustrated on a linear dynamical model for a buoy-type WEC with significant resonant modes in surge and pitch, and equipped with three spatially-distributed generators.     

Latching control of deep water wave energy devices using an active reference

This paper investigates latching type control on a floating wave energy converter in deep water. An on-board, actively controlled motion-compensated platform is used as a reference (‘active reference’) for power absorption and latching. A variational formulation is used to evaluate an optimal control sequence in the time domain. Time domain simulation results are presented for a heaving buoy in small-amplitude waves. Results are compared with an equivalent system where latching and power absorption are from a sea-bottom-fixed reference.