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The book, "Optimization and Energy Maximizing Control Systems for Wave Energy Converters", presents eleven contributions on the latest scientific advancements of 2020-2021 in wave energy technology optimization and control, including holistic techno-economic optimization, inclusion of nonlinear effects, and real-time implementations of estimation and control algorithms.
The book, “Optimization and Energy Maximizing Control Systems for Wave Energy Converters”, presents eleven contributions on the latest scientific advancements of 2020-2021 in wave energy technology optimization and control, including holistic techno-economic optimization, inclusion of nonlinear effects, and real-time implementations of estimation and control algorithms.
Abstract : Wave Energy Converter Array is a practical approach to harvest ocean wave energy. To leverage the potential of the WEC array in terms of energy extraction, it is essential to have a properly designed array configuration and control system. This thesis explores the optimal configuration of Wave Energy Converters (WECs) arrays and their optimal control. The optimization of the WEC array allows both dimensions of individual WECs as well as the array layout to varying. In the first optimization problem, cylindrical buoys are assumed in the array where their radii and drafts are optimization parameters. Genetic Algorithms are used for optimization. Three case studies are investigated of different array sizes: 3, 5, and 7 devices in the array. Two types of controls are assumed; the first is the standard impedance matching control while the second is a derivative control. The numerical test cases demonstrate that a higher q-factor is achieved when optimizing the buoys dimensions simultaneously with the array layout. In the conducted test cases, it is shown that optimizing the array layout can increase the q-factor on average by 39.21% when using optimal control, and increase it on average by a factor of 8.87% when using a derivative control. Arrays of wave energy converters (WECs) usually have large spacing between members of the array to avoid negative hydrodynamic interaction between members in the array. Errors in estimating the spacing between members may result in a significant degradation in the performance of the array in terms of the total harvested energy, due to destructive hydrodynamic interaction between members of the array. In this thesis, a hybrid design of wave energy converter arrays, that contains two types of WECs, the heaving buoys, and the floating flap-type devices, is investigated and compared against traditional WEC arrays of heaving buoys. The resulting q-factor is less sensitive to deviations in the spacing from the design layout. This hybrid array, hence, enables more WECs in the same ocean area. The two types of arrays are tested using 40 layouts that have different separation distances ranging from small to large. With the hybrid configuration, the array achieved a variance of the q-factor as low as 0.006. The traditional array has a variance of 0.024 which is four times larger. The optimization is conducted on the hybrid array with both layout and dimension as design variables. The optimal control algorithm for the WEC array is developed using the optimality condition. Devices in the array are assumed to be identical heaving buoys. The optimization objective is to maximize energy extraction at each time step. Both regular and irregular waves are used to excite the array. The unconstrained optimal control problem is solved with saturation on the control force. The solutions show that good wave estimations and sufficient accuracy of the radiation sub-system are the keys to the desired WEC array performance.
Abstract : In this dissertation, we address the optimal control and shape optimization of Wave Energy Converters. The wave energy converters considered in this study are the single-body heaving wave energy converters, and the two-body heaving wave energy converters. Different types of wave energy converters are modeled mathematically, and different optimal controls are developed for them. The concept of shape optimization is introduced in this dissertation; the goal is to leverage nonlinear hydrodynamic forces which are dependent on the buoy shape. In this dissertation, shape optimization is carried out and its impact on energy extraction is investigated. In all the studies conducted in this dissertation the objective is set to maximize the harvested energy, in various wave climates. The development of a multi-resonant feedback controller is first introduced which targets both amplitude and phase through feedback that is constructed from individual frequency components that comes from the spectral of the measurements signal. Each individual frequency uses a Proportional-Derivative control to provide both optimal resistive and reactive elements. Two-body heaving pointer absorbers are also investigated. Power conversion is from the relative have oscillation between the two bodies. The oscillation is controlled on a wave-by-wave basis using near-optimal feed-forward control. Chapter 4 presents the dynamic formulation used to evaluate the near-optimal, wave-by-wave control forces in the time domain. Also examined are the reaction-frame geometries for their impact on overall power capture through favorable hydrodynamic inter-actions. Performance is evaluated in a range of wave conditions sampled over a year at a chosen site of deployment. It is found that control may be able to provide the required amounts of power to sustain instrument operation at the chosen site, but also that energy storage options be worth pursuing. Chapter 5 presents an optimization approach to design axisymmetric wave energy converters (WECs) based on a non-linear hydrodynamic model. The time domain nonlinear Froude-Krylov force can be computed for a complex buoy shape, by adopting analytical formulas of its basic shape components. The time domain Forude-Krylov force is decomposed into its dynamic and static components, and then contribute to the calculation of the excitation force and the hydro-static force. A non-linear control is assumed in the form of the combination of linear and non-linear damping terms. A variable size genetic algorithm (GA) optimization tool is developed to search for the optimal buoy shape along with the optimal control coefficients simultaneously. Chromosome of the GA tool is designed to improve computational efficiency and to leverage variable size genes to search for the optimal non-linear buoy shape. Different criteria of wave energy conversion can be implemented by the variable size GA tool. Simulation results presented in this thesis show that it is possible to find non-linear buoy shapes and non-linear controllers that take advantage of non-linear hydrodynamics to improve energy harvesting efficiency with out adding reactive terms to the system.
Wave energy offers a promising renewable energy source, however, technologies converting wave energy into useful electricity face many design challenges. This guide presents numerical modelling and optimization methods for the development of wave energy converter technologies, from principles to applications. It covers the development status and perspectives of wave energy converter systems; the fundamental theories on wave power absorption; the modern wave energy converter concepts including oscillating bodies in single and multiple degree of freedom and oscillating water column technologies; 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 www.routledge.com has been made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license.
With this self-contained and comprehensive text, students and researchers will gain a detailed understanding of the fundamental aspects of the hydrodynamic control of wave energy converters. Such control is necessary to maximise energy capture for a given device configuration and plays a major role in efforts to make wave energy economic. Covering a wide range of disciplines, the reader is taken from the mathematical and technical fundamentals, through the main pillars of wave energy hydrodynamic control, right through to state-of-the-art algorithms for hydrodynamic control. The various operating principles of wave energy converters are exposed and the unique aspects of the hydrodynamic control problem highlighted, with a variety of potential solutions discussed. Supporting material on wave forecasting and the interaction of the hydrodynamic control problem with other aspects of wave energy device optimisation, such as device geometry optimisation and optimal device array layout, is also provided.
This thesis deals with the optimal control of wave energy converters and some associated observer design problems. The first part of the thesis will investigate model predictive control of an ocean wave energy converter to maximize extracted power. A generic heaving converter that can have both linear dampers and active elements as a power take-off system is considered and an efficient optimal control algorithm is developed for use within a receding horizon control framework. The optimal control is also characterized analytically. A direct transcription of the optimal control problem is also considered as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard nonlinear program solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is shown not to be a quadratic program. Results are compared with other methods like optimal latching to demonstrate the improvement in absorbed power under irregular sea condition simulations. In the second part, robust estimation of the radiation forces and states inherent in the optimal control of wave energy converters is considered. Motivated by this, low order H∞ observer design for bilinear systems with input constraints is investigated and numerically tractable methods for design are developed. A bilinear Luenberger type observer is formulated and the resulting synthesis problem reformulated as that for a linear parameter varying system. A bilinear matrix inequality problem is then solved to find nominal and robust quadratically stable observers. The performance of these observers is compared with that of an extended Kalman filter. The robustness of the observers to parameter uncertainty and to variation in the radiation subsystem model order is also investigated. This thesis also explores the numerical integration of bilinear control systems with zero-order hold on the control inputs. Making use of exponential integrators, exact to high accuracy integration is proposed for such systems. New a priori bounds are derived on the computational complexity of integrating bilinear systems with a given error tolerance. Employing our new bounds on computational complexity, we propose a direct exponential integrator to solve bilinear ODEs via the solution of sparse linear systems of equations. Based on this, a novel sparse direct collocation of bilinear systems for optimal control is proposed. These integration schemes are also used within the indirect optimal control method discussed in the first part.
Abstract : 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.
The authors of this timely reference provide an updated and global view on ocean wave energy conversion – and they do so for wave energy developers as well as for students and professors. The book is orientated to the practical solutions that this new industry has found so far and the problems that any device needs to face. It describes the actual principles applied to machines that convert wave power to electricity and examines state-of-the-art modern systems.