Optimal control of wave energy converters

Wave Energy Converters (WECs) are devices designed to absorb energy from ocean waves. The particular type of Wave Energy Converter (WEC) considered in this thesis is an oscillating body; energy conversion is carried out by means of a structure immersed in water which oscillates under forces exerted by waves. This thesis addresses the control of oscillating body WECs and the objective of the control system is to optimise the motion of the devices that maximises the energy absorption. In particular, this thesis presents the formulation of the optimal control problem for WECs in the framework of direct transcription methods, known as spectral and pseudospectral optimal control. Direct transcription methods transform continuous time optimal control problems into Non Linear Programming (NLP) problems, for which the literature (and the market) offer a large number of standard algorithms (and software packages). It is shown, in this thesis, that direct transcription gives the possibility of formulating complex control problems where realistic scenarios can be taken into account, such as physical limitations and nonlinearities in the behaviour of the devices. Additionally, by means of spectral and pseudospectral methods, it is possible to find an approximation of the optimal solution directly from sampled frequency and impulse response models of the radiation forces, obviating the need for finite order approximate models. By implementing a spectral method, convexity of the NLP problem, associated with the optimal control problem for a single body WEC described by a linear model, is demonstrated analytically. The solution to a nonlinear optimal control problem is approximated by means of pseudospectral optimal control. In the nonlinear case, simulation results show a significant difference in the optimal behaviour of the device, both in the motion and in the energy absorption, when the quadratic term describing the viscous forces are dominant, compared to the linear case. This thesis also considers the comparison of two control strategies for arrays of WECs. A Global Control strategy computes the optimal motion by taking into account the complete model of the array and it provides the global optimum for the absorbed energy. In contrast, an Independent Control strategy implements a control system on each device which is independent from all the other devices. The final part of the thesis illustrates an approach for the study of the effects of constraints on the total absorbed energy. The procedure allows the feasibility of the constrained energy maximisation problem to be studied, and it provides an intuitive framework for the design of WECs relating to the power take-off operating envelope, thanks to the geometrical interpretation of the functions describing both the total absorbed energy and the constraints

CLOSED LOOP ENERGY MAXIMIZING CONTROL OF A WAVE ENERGY CONVERTER USING AN ESTIMATED LINEAR MODEL THAT APPROXIMATES THE NONLINEAR FROUDE-KRYLOV FORCE

Wave energy converters (WECs) exploit ocean wave energy and convert it into useful forms such as electricity. But for WECs to be successful on a large scale, two primary conditions need to be satisfied. The energy generated must satisfy the network requirements, and second, energy flow from waves to the grid needs to be maximized. In this dissertation, we address the second problem. Most control techniques for WECs today use the Cummins\u27 linear model to simulate WEC hydrodynamics. However, it has been shown that under the application of a control force, where WEC motions are amplified, the linear model diverges from actual motions. Hence, it becomes necessary to model the nonlinear motion for realistic energy capture prediction. In this work, it is shown that a closed form energy optimal solution to the nonlinear model requires satisfaction of initial conditions that violate physical restrictions. Numerical optimization based controllers that use physical constraints as a necessary condition require large computation costs and are difficult to implement in real time. To mitigate computation costs for real-time implementation while precisely predicting nonlinear behavior, an efficient method of modelling WECs using an estimated linear model for computing the energy optimal control solution is presented. The estimated linear model is compared against the Cummins\u27 model for accuracy of motion during an uncontrolled case. It is also shown that, there exists a force which results in higher energy extraction than optimal force from Cummins\u27 model when applied to a nonlinear model. Additional analyses are also performed to evaluate the robustness of the proposed method in random and extreme sea states

Optimal control of wave energy converters

Wave Energy Converters (WECs) are devices designed to absorb energy from ocean waves. The particular type of Wave Energy Converter (WEC) considered in this thesis is an oscillating body; energy conversion is carried out by means of a structure immersed in water which oscillates under forces exerted by waves. This thesis addresses the control of oscillating body WECs and the objective of the control system is to optimise the motion of the devices that maximises the energy absorption. In particular, this thesis presents the formulation of the optimal control problem for WECs in the framework of direct transcription methods, known as spectral and pseudospectral optimal control. Direct transcription methods transform continuous time optimal control problems into Non Linear Programming (NLP) problems, for which the literature (and the market) offer a large number of standard algorithms (and software packages). It is shown, in this thesis, that direct transcription gives the possibility of formulating complex control problems where realistic scenarios can be taken into account, such as physical limitations and nonlinearities in the behaviour of the devices. Additionally, by means of spectral and pseudospectral methods, it is possible to find an approximation of the optimal solution directly from sampled frequency and impulse response models of the radiation forces, obviating the need for finite order approximate models. By implementing a spectral method, convexity of the NLP problem, associated with the optimal control problem for a single body WEC described by a linear model, is demonstrated analytically. The solution to a nonlinear optimal control problem is approximated by means of pseudospectral optimal control. In the nonlinear case, simulation results show a significant difference in the optimal behaviour of the device, both in the motion and in the energy absorption, when the quadratic term describing the viscous forces are dominant, compared to the linear case. This thesis also considers the comparison of two control strategies for arrays of WECs. A Global Control strategy computes the optimal motion by taking into account the complete model of the array and it provides the global optimum for the absorbed energy. In contrast, an Independent Control strategy implements a control system on each device which is independent from all the other devices. The final part of the thesis illustrates an approach for the study of the effects of constraints on the total absorbed energy. The procedure allows the feasibility of the constrained energy maximisation problem to be studied, and it provides an intuitive framework for the design of WECs relating to the power take-off operating envelope, thanks to the geometrical interpretation of the functions describing both the total absorbed energy and the constraints

Towards data-driven and data-based control of wave energy systems: Classification, overview, and critical assessment

Currently, a significant effort in the world research panorama is focused on finding efficient solutions to a carbon-free energy supply, wave energy being one of the most promising sources of untapped renewable energy. However, wave energy is not currently economic, though control technology has been shown to significantly increase the energy capture capabilities. Usually, the synthesis of a wave energy control strategy requires the adoption of control-oriented models, which are prone to error, particularly arising from unmodelled hydrodynamics, given the complexity of the hydrodynamic interactions between the device and the ocean. In this context, data-driven and data-based control strategies provide a potential solution to some of these issues, using real-time data to gather information about the system dynamics and performance. Thus motivated, this study provides a detailed analysis of different approaches to the exploitation of data in the design of control philosophies for wave energy systems, establishing clear definitions of data-driven and data-based control in this field, together with a classification highlighting the various roles of data in the control synthesis process. In particular, we investigate intrinsic opportunities and limitations behind the use of data in the process of control synthesis, providing a comprehensive review together with critical considerations aimed at directly contributing towards the development of efficient data-driven and data-based control systems for wave energy devices

Wave force prediction effect on the energy absorption of a wave energy converter with real-time control

Real-time control has been widely adopted to enlarge the energy extraction of a wave energy converter (WEC). In order to implement a real-time control, it is necessary to predict the wave excitation forces in the close future. In many previous studies, the wave forces over the prediction horizon were assumed to be already known, while the wave force prediction effect has been hardly examined. In this paper, we investigate the effect of wave force prediction on the energy absorption of a heaving point-absorber WEC with real-time latching control. The real-time control strategy is based on the combination of optimal command theory and first order-one variable grey model GM(1,1). It is shown that a long prediction horizon is beneficial to the energy absorption whereas the prediction deviation reduces extracting efficiency of the WEC. Further analysis indicates that deviation of wave force amplitude has little influence on the WEC performance. It is the phase deviation that leads to energy loss. Since the prediction deviation accumulates over the horizon, a moderate horizon is thus recommended

Optimization and Energy Maximizing Control Systems for Wave Energy Converters

In recent years, we have been witnessing great interest and activity in the field of wave energy converters’ (WECs) development, striving for competitiveness and economic viability via increasing power conversion while decreasing costs and ensuring survivability [...

Empowering wave energy with control technology: Possibilities and pitfalls

With an increasing focus on climate action and energy security, an appropriate mix of renewable energy technologies is imperative. Despite having considerable global potential, wave energy has still not reached a state of maturity or economic competitiveness to have made an impact. Challenges include the high capital and operational costs associated with deployment in the harsh ocean environment, so it is imperative that the full energy harnessing capacity of wave energy devices, and arrays of devices in farms, is realised. To this end, control technology has an important role to play in maximising power capture, while ensuring that physical system constraints are respected, and control actions do not adversely affect device lifetime. Within the gamut of control technology, a variety of tools can be brought to bear on the wave energy control problem, including various control strategies (optimal, robust, nonlinear, etc.), data-based model identification, estimation, and forecasting. However, the wave energy problem displays a number of unique features which challenge the traditional application of these techniques, while also presenting a number of control ‘paradoxes’. This review articulates the important control-related characteristics of the wave energy control problem, provides a survey of currently applied control and control-related techniques, and gives some perspectives on the outstanding challenges and future possibilities. The emerging area of control co-design, which is especially relevant to the relatively immature area of wave energy system design, is also covered

Control techniques for ocean energy applications.

Control systems, despite often being `invisibly' incorporated within products, devices and vehicles, are ubiquitous. They are prevalent within the automotive and aerospace industries and form part of the vanguard of technologies in in- creasing performance, improving fuel economy and increasing safety. One of the most appealing aspects of incorporating control technology in many systems is that the addition of extra control functionality can usually be achieved merely through the addition of extra software code though, in many cases, additional sensors and actuators may be required. This relatively simple implementation modality masks both the capability of control systems and the high level of engineering underpinning the devel- opment of a suitable control algorithm. For example, many high-performance model-based control design methods require an accurate mathematical model of the system to be controlled and a significant number of man-hours can be absorbed in modelling. Nevertheless, there is usually a good case to be made for the incorporation of control technology to improve the performance (both technical and economic), reliability and safety of a system. In this chapter, we will examine the role that control engineering can play in making ocean energy technology more competitive

Maximization of energy absorption for a wave energy converter using the deep machine learning

A controller is usually used to maximize the energy absorption of wave energy converter. Despite the development of various control strategies, the practical implementation of wave energy control is still difficult since the control inputs are the future wave forces. In this work, the artificial intelligence technique is adopted to tackle this problem. A multi-layer artificial neural network is developed and trained by the deep machine learning algorithm to forecast the short-term wave forces. The model predictive control strategy is used to implement real-time latching control action to a heaving point-absorber. Simulation results show that the average energy absorption is increased substantially with the controller. Since the future wave forces are predicted, the controller is applicable to a full-scale wave energy converter in practice. Further analysis indicates that the prediction error has a negative effect on the control performance, leading to the reduction of energy absorption