High-capacity wave energy conversion by multi-floats, multi-PTO, control and prediction: generalised state-space modelling with linear optimal control and arbitrary headings

Wave energy converters with capacity similar to, or greater than, wind turbines are desirable for the supply of electricity to the grid. It is shown that this may be provided by multiple floats in a hinged raft-type configuration with multimode forcing. The case analysed has 8 floats and 4 power take off (PTO) units. Analysis is based on linear diffraction-radiation modelling, validated in wave basin experiments with a smaller number of floats. Control is desirable to improve energy capture, mainly demonstrated for point absorbers, but this has not previously been applied to such a complex problem with many freedoms. The linear hydrodynamic model in a state-space form makes it possible to implement advanced control algorithms in real time. Linear non-causal optimal control (LNOC) is applied with wave force prediction from auto-regression. For the design case with zero heading, as the configuration heads naturally into the wave direction, energy capture is improved by between 21% and 83%. The energy capture is about 62% the maximum possible from idealised analyses. Off-design, non-zero headings are also analysed to indicate how energy capture can be reduced; this is again improved by control, by several times at 90 degrees heading

Non-causal Linear Optimal Control with Adaptive Sliding Mode Observer for Multi-Body Wave Energy Converters

As a non-causal optimal control problem, the performance of wave energy converter (WEC) control relies on the accuracy of the future incoming wave prediction. However, the inevitable prediction errors can degrade WEC performance dramatically especially when a long prediction horizon is needed by a WEC non-causal optimal controller. This paper proposes a novel non-causal linear optimal control with adaptive sliding mode observer (NLOC+ASMO) scheme, which can effectively mitigate the control performance degradation caused by wave prediction errors. This advantage is achieved by embedding the following enabling techniques into the scheme: (i) an adaptive sliding mode observer (ASMO) to estimate current excitation force in real-time with explicitly formulated boundary of estimation error, (ii) an auto-regressive (AR) model to predict the incoming excitation force with explicitly formulated boundary of prediction error using a set of latest historical data of ASMO estimations from (i), and (iii) a compensator to compensate for both the estimation error and the prediction error of excitation force. Moreover, the proposed NLOC+ASMO scheme does not cause heavy computational load enabling its real-time implementation on standard computational hardware, which is especially critical for the control of WECs with complicated dynamics. The proposed NLOC+ASMO framework is generic and can be applied to a wide range of WECs, and in this paper we demonstrate the efficacy by using a multi-float and multi-motion WEC called M4 as a case study, whose control problem is more challenging than the widely studied point absorbers. Simulation results show the effectiveness of the proposed control scheme in a wide range of sea states, and it is also found that the controller is not sensitive to change of ASMO parameters

Modelling and Control of Multi-Mode Motion Ocean Wave Energy Converts.

PhD Theses.This thesis deals with the modelling and control problems for the multi-mode motion wave energy converters (WECs). This type of WEC has a higher potential power capture capability but involves hydrodynamic models of increased complexity. A typical multi-mode motion WEC, namely M4, is chosen for this case study. In the first part, the hydrodynamics of M4 are analysed. A control-oriented state-space model is then built for the purpose of controller design. This is done by firstly using the Euler-Lagrangian equation to derive the motion equation on a constrained coordinate. A system identification method is then introduced to model the radiation effects, and a model order reduction method is used to reduce the order of the radiation subsystems. The fidelity of the derived state-space model is validated against experimental data. In the second part, the linear non-causal optimal control (LNOC) framework is designed to tackle the energy maximising problem of the M4 WEC. This framework has three key components: a linear optimal controller, a Kalman filter with a random-walk wave-force model to estimate the system states and wave excitation force and an excitation-force predictor based on an autoregressive (AR) model. Their mathematical formulations are presented, followed by numerical simulations to demonstrate the control performance of the integrated framework. The results show that the AR wave excitation force predictor can provide preview wave force information accurately for around 2 peak periods of time, which is sufficient for control. The LNOC framework can effectively improve the energy conversion of M4 without introducing significant costs in terms of extra hardware components and 4 computational loads. In the last part, a variation of the M4 design, with four power take-offs (PTOs) instead of one, is studied. The goal is to showcase that the energy conversion capacity of a multi-PTO M-WEC, integrated with the LNOC framework, can be similar to that of an offshore wind turbine, which is desirable for electricity supply to the power grid. The effect of off-design, arbitrary WEC headings in various incoming wave direction is investigated as a vital sensitivity check to provide useful quantification for implementing the LNOC framework in practice. The improvement of captured power by the LNOC framework in all cases is shown to be substantial

Geometric optimization of a hinge-barge wave energy converter

Based on a small prototype of the McCabe wave pump device, this paper studies the optimal size of an interconnected pontoon system, where the power take-off systems attached to each barge are equipped with optimal linear passive dampers. To this end, an optimization procedure is developed, where the objective is to maximize the extracted energy of the device under given sea states. A multi-DOF mathematical model is presented to describe the device motion, and associated hydrodynamic parameters are computed using a boundary element model tool, based on linear potential flow theory. Numerical results, under regular and irregular waves, are presented. Simulation results show that the optimal dimension of the device, under given sea states, can be found using the developed methodology. In addition, it is found that the three-body hinge-barge device tends to perform like a two-body system under optimal control conditions. This indicates that a two-barge control system may be a better design solution in those situations, considering the high cost of power take-off systems

Modeling and Control of a Multibody Hinge-BargeWave Energy Converter

Wave Energy Converters (WECs) are devices used to extract energy from the waves. The particular WEC considered in this thesis is a three-body hinge-barge WEC, which is an articulated floating structure composed of 3 rectangular bodies interconnected by hinges, and it operates longitudinally to the direction to the incoming wave. The relative motion between each pair of bodies drives a Power Take-Off (PTO) system, which extracts the energy from the waves. The objective of this thesis is to increase the energy that can be extracted by a three-body hinge-barge WEC using an optimal control strategy, which computes the optimal loads applied by the PTOs driven by the relative motion between the bodies. The optimal control is formulated in the time domain, and computes the PTO loads in a coordinated way, so that the total energy extracted by the device is maximized. The optimal control strategy is formulated for a three-body hinge-barge WEC that is equipped with either passive or active PTOs. In this thesis, an optimal control strategy, for the maximization of the energy extracted by a three-body hinge-barge WEC, is derived with Pseudo-Spectral (PS) methods, which are a subset of the class of techniques used for the discretisation of integral and partial differential equations known as mean weighted residuals. In particular, PS methods based on Fourier basis functions, are used to derive an optimal control strategy, for a finite time horizon. Therefore, an optimal control strategy, with PS methods based on Fourier basis functions, cannot be applied for realtime control of the WEC, as Fourier basis functions can only represent the steady-state response of the WEC. However, PS methods based on Fourier basis functions provide a useful framework for the evaluation of the achievable power absorption performance of the WEC, with both active and passive PTOs. The Receding Horizon (RH) real-time optimal control of a three-body hingebarge WEC is derived with PS methods based on Half-Range Chebyshev-Fourier (HRCF) basis functions. The RH optimal real-time controller, with PS methods based on HRCF basis functions, maximizes the energy extracted by the WEC at each time step over a moving control horizon. In contrast to Fourier basis functions, HRCF basis functions are well suited for the approximation of non-periodic signals, allowing the representation of both the transient and steady-state response of the WEC. The optimal control strategy, with PS methods based on either Fourier or HRCF basis functions, is based on a dynamic model of the device, which is derived with two different modeling methodologies, that can be also applied to other types of multiple body WECs. The modeling methodologies are validated against wave-tank tests carried out on a 1/7th scale two-body hingebarge device, and a 1/25th and 1/20th scale three-body hinge-barge device

Geometric optimisation of wave energy conversion devices: A survey

Unlike more established renewable energy conversion technologies, such as wind turbines, wave power systems have reached neither commercial maturity, nor technological convergence. The significant variation in device geometries and operating principles has resulted in a diversification of effort, with little coordination or true comparative analysis. The situation is compounded by the relative lack of systematic optimisation applied to the sector, partly explained by the complexity and uncertainty associated with wave energy system models, as well as difficulties in the evaluation of appropriate target function metrics. This review provides a critical overview of the state-of-the-art in wave energy device geometry optimisation, comparing and contrasting various optimisation approaches, and attempting to detail the current limitations preventing further progress, and convergence, in the development of optimal wave energy technology

Modelling and Optimization of Wave Energy Converters

Wave energy offers a promising renewable energy source. This guide presents numerical modelling and optimisation methods for the development of wave energy converter technologies, from principles to applications. It covers oscillating water column technologies, theoretical wave power absorption, heaving point absorbers in single and multi-mode degrees of freedom, and the relatively hitherto unexplored topic of wave energy harvesting farms. It can be used as a specialist student textbook as well as a reference book for the design of wave energy harvesting systems, across a broad range of disciplines, including renewable energy, marine engineering, infrastructure engineering, hydrodynamics, ocean science, and mechatronics engineering. The Open Access version of this book, available at https://www.routledge.com/ has been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license

Optimal Control of Wave Energy Converters

In this dissertation, we address the optimal control of the Wave Energy Converters. The Wave Energy Converters introduced in this study can be categorized as the single body heaving device, the single body pitching device, the single body three degrees of freedoms device, and the Wave Energy Converters array. Different types of Wave Energy Converters are modeled mathematically, and different optimal controls are developed for them. The objective of the optimal controllers is to maximize the energy extraction with and without the motion and control constraints. The development of the unconstrained control is first introduced which includes the implementation of the Singular Arc control and the Simple Model Control. The constrained optimal control is then introduced which contains the Shape-based approach, Pseudospectral control, the Linear Quadratic Gaussian optimal control, and the Collective Control. The wave estimation is also discussed since it is required by the controllers. Several estimators are implemented, such as the Kalman Filter, the Extended Kalman Filter, and the Kalman-Consensus Filter. They can be applied for estimating the system states and the wave excitation force/wave excitation force field. Last, the controllers are validated with the Discrete Displacement Hydraulic system which is the Power Take-off unit of the Wave Energy Converter. The simulation results show that the proposed optimal controllers can maximize the energy absorption when the wave estimation is accurate. The performance of the unconstrained controllers is close to the theoretical maximum (Complex Conjugate Control). Furthermore, the energy extraction is optimized and the constraints are satisfied by applying the constrained controllers. However, when the proposed controllers are further validated with the hydraulic system, they extract less energy than a simple Proportional-derivative control. This indicates the dynamics of the Power take-off unit needs to be considered in designing the control to obtain the robustness

Robust Excitation Force Estimation and Prediction for Wave Energy Converter M4 Based on Adaptive Sliding-Mode Observer

The wave excitation force estimation and prediction play an important role in improving the performance of causal and noncausal controllers for wave energy converters (WECs). This article proposes a robust adaptive sliding-mode observer (ASMO) to estimate the wave excitation force subject to unknown disturbances and parametric uncertainties for a multimotion multifloat WEC, called M4. Both the convergence time and the estimation error can be explicitly bounded within expected limits by tuning the ASMO parameters, which are essentially beneficial for causal controllers to maintain the control performance. A fixed-time convergent sliding variable is designed to drive the estimation error into a small region within a fixed time. Due to the adaptive law, the overall system is proven to be finite-time stable, which allows explicit formulations of the convergence time and the estimation error. Moreover, based on the wave force estimation by the ASMO, an improved auto-regressive (AR) model whose coefficients are updated by online training is developed to predict the wave excitation force. The prediction errors can also be explicitly estimated to achieve guaranteed control performance for the noncausal controller requiring future excitation force. From the comparison based on a realistic sea wave gathered from Cornwall, U.K., it can be found that compared with the conventional Kalman filter, the ASMO achieves a smaller steady-state estimation error and has satisfactory robustness performance against 30% model mismatch.</p